Lcm of 42 and 54

Lcm of 42 and 54 DEFAULT

The lcm of 54 and 42 is the smallest positive integer that divides the numbers 54 and 42 without a remainder. Spelled out, it is the least common multiple of 54 and 42. Here you can find the lcm of 54 and 42, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 54 and 42, but also that of three or more integers including fifty-four and forty-two for example. Keep reading to learn everything about the lcm (54,42) and the terms related to it.

What is the LCM of 54 and 42

If you just want to know what is the least common multiple of 54 and 42, it is 378. Usually, this is written as

lcm(54,42) = 378

The lcm of 54 and 42 can be obtained like this:

  • The multiples of 54 are … , 324, 378, 432, ….
  • The multiples of 42 are …, 336, 378, 420, …
  • The common multiples of 54 and 42 are n x 378, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}.
  • In the intersection multiples of 54 ∩ multiples of 42 the least positive element is 378.
  • Therefore, the least common multiple of 54 and 42 is 378.

Taking the above into account you also know how to find all the common multiples of 54 and 42, not just the smallest. In the next section we show you how to calculate the lcm of fifty-four and forty-two by means of two more methods.

How to find the LCM of 54 and 42

The least common multiple of 54 and 42 can be computed by using the greatest common factor aka gcf of 54 and 42. This is the easiest approach:

lcm (54,42) = \frac{54 \times 42}{gcf(54,42)} = \frac{2268}{6} = 378

Alternatively, the lcm of 54 and 42 can be found using the prime factorization of 54 and 42:

  • The prime factorization of 54 is: 2 x 3 x 3 x 3
  • The prime factorization of 42 is: 2 x 3 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(54,54) = 378

In any case, the easiest way to compute the lcm of two numbers like 54 and 42 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 54,42. Push the button only to start over.

Similar searched terms on our site also include:

Use of LCM of 54 and 42

What is the least common multiple of 54 and 42 used for? Answer: It is helpful for adding and subtracting fractions like 1/54 and 1/42. Just multiply the dividends and divisors by 7 and 9, respectively, such that the divisors have the value of 378, the lcm of 54 and 42.

\frac{1}{54} + \frac{1}{42} = \frac{7}{378} + \frac{9}{378} = \frac{16}{378}. \frac{1}{54} - \frac{1}{42} = \frac{7}{378} - \frac{9}{378} = \frac{-2}{378}.

Properties of LCM of 54 and 42

The most important properties of the lcm(54,42) are:

  • Commutative property: lcm(54,42) = lcm(42,54)
  • Associative property: lcm(54,42,n) = lcm(lcm(42,54),n) n\neq 0 \thinspace\in\thinspace\mathbb{Z}

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 54 and 42 is 378. In common notation: lcm (54,42) = 378.

If you have been searching for lcm 54 and 42 or lcm 54 42 then you have come to the correct page, too. The same is the true if you typed lcm for 54 and 42 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including fifty-four / forty-two by using the search form in the sidebar of this page.

Questions and comments related to the lcm of 54 and 42 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the least common multiple of 54 and 42 has been useful to you, and make sure to bookmark our site.

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The LCM of 42 and 54 is 378.

Steps to find LCM

  1. Find the prime factorization of 42
    42 = 2 × 3 × 7
  2. Find the prime factorization of 54
    54 = 2 × 3 × 3 × 3
  3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

    LCM = 2 × 3 × 3 × 3 × 7
  4. LCM = 378

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Find least common multiple (LCM) of: 84 & 10821 & 27126 & 16214 & 18210 & 270294 & 37884 & 5442 & 108126 & 5442 & 162210 & 5442 & 270294 & 5442 & 378

LCM Calculator

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

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The lcm of 42 and 54 is the smallest positive integer that divides the numbers 42 and 54 without a remainder. Spelled out, it is the least common multiple of 42 and 54. Here you can find the lcm of 42 and 54, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 42 and 54, but also that of three or more integers including forty-two and fifty-four for example. Keep reading to learn everything about the lcm (42,54) and the terms related to it.

What is the LCM of 42 and 54

If you just want to know what is the least common multiple of 42 and 54, it is 378. Usually, this is written as

lcm(42,54) = 378

The lcm of 42 and 54 can be obtained like this:

  • The multiples of 42 are … , 336, 378, 420, ….
  • The multiples of 54 are …, 324, 378, 432, …
  • The common multiples of 42 and 54 are n x 378, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}.
  • In the intersection multiples of 42 ∩ multiples of 54 the least positive element is 378.
  • Therefore, the least common multiple of 42 and 54 is 378.

Taking the above into account you also know how to find all the common multiples of 42 and 54, not just the smallest. In the next section we show you how to calculate the lcm of forty-two and fifty-four by means of two more methods.

How to find the LCM of 42 and 54

The least common multiple of 42 and 54 can be computed by using the greatest common factor aka gcf of 42 and 54. This is the easiest approach:

lcm (42,54) = \frac{42 \times 54}{gcf(42,54)} = \frac{2268}{6} = 378

Alternatively, the lcm of 42 and 54 can be found using the prime factorization of 42 and 54:

  • The prime factorization of 42 is: 2 x 3 x 7
  • The prime factorization of 54 is: 2 x 3 x 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(42,42) = 378

In any case, the easiest way to compute the lcm of two numbers like 42 and 54 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 42,54. Push the button only to start over.

Similar searched terms on our site also include:

Use of LCM of 42 and 54

What is the least common multiple of 42 and 54 used for? Answer: It is helpful for adding and subtracting fractions like 1/42 and 1/54. Just multiply the dividends and divisors by 9 and 7, respectively, such that the divisors have the value of 378, the lcm of 42 and 54.

\frac{1}{42} + \frac{1}{54} = \frac{9}{378} + \frac{7}{378} = \frac{16}{378}. \frac{1}{42} - \frac{1}{54} = \frac{9}{378} - \frac{7}{378} = \frac{2}{378}.

Properties of LCM of 42 and 54

The most important properties of the lcm(42,54) are:

  • Commutative property: lcm(42,54) = lcm(54,42)
  • Associative property: lcm(42,54,n) = lcm(lcm(54,42),n) n\neq 0 \thinspace\in\thinspace\mathbb{Z}

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 42 and 54 is 378. In common notation: lcm (42,54) = 378.

If you have been searching for lcm 42 and 54 or lcm 42 54 then you have come to the correct page, too. The same is the true if you typed lcm for 42 and 54 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including forty-two / fifty-four by using the search form in the sidebar of this page.

Questions and comments related to the lcm of 42 and 54 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the least common multiple of 42 and 54 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email
Sours: https://timestable.net/lcm-of-42-and-54
LCM of 42 54 and 78 by Division Method in Urdu, LCM of 42 54 and 78

LCM of 42 and 54

FAQs on LCM of 42 and 54

What is the LCM of 42 and 54?

The LCM of 42 and 54 is 378. To find the least common multiple of 42 and 54, we need to find the multiples of 42 and 54 (multiples of 42 = 42, 84, 126, 168 . . . . 378; multiples of 54 = 54, 108, 162, 216 . . . . 378) and choose the smallest multiple that is exactly divisible by 42 and 54, i.e., 378.

How to Find the LCM of 42 and 54 by Prime Factorization?

To find the LCM of 42 and 54 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (54 = 2 × 3 × 3 × 3). LCM of 42 and 54 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 54.
⇒ LCM of 42, 54 = 21 × 33 × 71 = 378.

Which of the following is the LCM of 42 and 54? 3, 25, 42, 378

The value of LCM of 42, 54 is the smallest common multiple of 42 and 54. The number satisfying the given condition is 378.

What are the Methods to Find LCM of 42 and 54?

The commonly used methods to find the LCM of 42 and 54 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method

If the LCM of 54 and 42 is 378, Find its GCF.

LCM(54, 42) × GCF(54, 42) = 54 × 42
Since the LCM of 54 and 42 = 378
⇒ 378 × GCF(54, 42) = 2268
Therefore, the greatest common factor = 2268/378 = 6.

 

Sours: https://www.cuemath.com/numbers/lcm-of-42-and-54/

And lcm of 54 42

What is the Least Common Multiple of 42 and 54?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 42 and 54 is 378.

LCM(42,54) = 378

Least Common Multiple of 42 and 54 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 54, than apply into the LCM equation.

GCF(42,54) = 6
LCM(42,54) = ( 42 × 54) / 6
LCM(42,54) = 2268 / 6
LCM(42,54) = 378

Least Common Multiple (LCM) of 42 and 54 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 54. First we will calculate the prime factors of 42 and 54.

Prime Factorization of 42

Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:

42 = 21 × 31 × 71

Prime Factorization of 54

Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:

54 = 21 × 33

Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 54.

LCM(42,54) = 21 × 33 × 71
LCM(42,54) = 378

Related Least Common Multiples of 42

Related Least Common Multiples of 54

Sours: https://www.gcflcm.com/lcm-of-42-and-54
Finding LCM using prime factorisation

What is the Least Common Multiple of 42 and 54?

The LCM (least common multiple) of the numbers 42 and 54 is 378

See calculation

Least Common Multiple  of 42 and 54 is 378

How to find the Least Common Multiple of 42 and 54?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 42 and 54.

Follow the steps below, and let's calculate the LCM of 42 and 54.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 42 and 54:

Prime factors of 42

The prime factors of 42 are 2, 3 and 7. Prime factorization of 42 in exponential form is:

42 = 21x31x71

Prime factors of 54

The prime factors of 54 are 2, 3, 3 and 3. Prime factorization of 54 in exponential form is:

54 = 21x33


Step 2: Identify the highest power of each prime number from the above boxes:


Step 3: Multiply these values together:


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 42 and 54.

The Least Common Multiple of 42 and 54 is 378.


Method 2 - List of Multiples

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.


Multiples of 42:

42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504

Multiples of 54:

54, 108, 162, 216, 270, 324, 378, 432, 486, 540


Therefore,

Sours: https://www.gcf-lcm.com/lcm-of-42-54/

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The Least Common Multiple (LCM) of 42 and 54 is the smallest positive number that is a multiple of both 42 and 54.

Here we will show you two different ways to figure out the Least Common Multiple of 42 and 54.

Our favorite way is to find the prime factors of each number and then merge them together to get the answer.

The prime factor(s) of 42 are:
2 x 3 x 7

The prime factor(s) of 54 are:
2 x 3 x 3 x 3

Merging them together using the least amount of factors, you get:

2 x 3 x 3 x 3 x 7

Then you can multiply those numbers together to get the Least Common Multiple (LCM) of 42 and 54 as follows:

378


To find the Least Common Multiple of 42 and 54, you can also make a list of multiples of 42 and a list of multiples of 54.

Multiples of 42 would be 42, 84, 126, 168 and so on.

Multiples of 54 would be 54, 108, 162, 216 and so on.

Now, compare the two lists to find the smallest number the two lists have in common, which is the Least Common Multiple of 42 and 54. You will once again see that the answer will be:

378

What is the Least Common
Multiple of 42 and 55?
Go here for the next Least Common Multiple on our list that we calculated.

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