LCM the 7 and 8 is the the smallest number amongst all typical multiples of 7 and 8. The first few multiples the 7 and 8 space (7, 14, 21, 28, . . . ) and also (8, 16, 24, 32, 40, 48, 56, . . . ) respectively. There are 3 generally used approaches to uncover LCM of 7 and also 8 - through listing multiples, by element factorization, and also by division method.

You are watching: What is the least common multiple of 7 and 8

1.LCM of 7 and 8
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 7 and 8 is 56.

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Explanation:

The LCM of two non-zero integers, x(7) and also y(8), is the smallest hopeful integer m(56) the is divisible by both x(7) and also y(8) without any type of remainder.


Let's look in ~ the different methods for finding the LCM that 7 and 8.

By element Factorization MethodBy department MethodBy Listing Multiples

LCM of 7 and 8 by prime Factorization

Prime factorization of 7 and also 8 is (7) = 71 and also (2 × 2 × 2) = 23 respectively. LCM of 7 and also 8 deserve to be acquired by multiplying prime factors raised to your respective highest power, i.e. 23 × 71 = 56.Hence, the LCM that 7 and also 8 by prime factorization is 56.

LCM that 7 and also 8 by division Method

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To calculate the LCM the 7 and 8 by the department method, we will divide the numbers(7, 8) by your prime determinants (preferably common). The product of these divisors gives the LCM of 7 and also 8.

Step 3: continue the actions until just 1s room left in the last row.

The LCM of 7 and 8 is the product of all prime numbers on the left, i.e. LCM(7, 8) by department method = 2 × 2 × 2 × 7 = 56.

LCM of 7 and also 8 by Listing Multiples

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To calculation the LCM of 7 and 8 by listing out the typical multiples, we deserve to follow the given listed below steps:

Step 1: list a few multiples that 7 (7, 14, 21, 28, . . . ) and 8 (8, 16, 24, 32, 40, 48, 56, . . . . )Step 2: The usual multiples native the multiples the 7 and 8 room 56, 112, . . .Step 3: The smallest common multiple that 7 and 8 is 56.

∴ The least usual multiple of 7 and 8 = 56.

☛ also Check:


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FAQs on LCM that 7 and also 8

What is the LCM of 7 and 8?

The LCM the 7 and also 8 is 56. To discover the LCM the 7 and 8, we require to uncover the multiples the 7 and also 8 (multiples that 7 = 7, 14, 21, 28 . . . . 56; multiples that 8 = 8, 16, 24, 32 . . . . 56) and also choose the the smallest multiple that is precisely divisible through 7 and also 8, i.e., 56.

What is the the very least Perfect Square Divisible by 7 and 8?

The the very least number divisible by 7 and also 8 = LCM(7, 8)LCM the 7 and 8 = 2 × 2 × 2 × 7 ⇒ least perfect square divisible by each 7 and 8 = LCM(7, 8) × 2 × 7 = 784 Therefore, 784 is the compelled number.

What is the Relation between GCF and LCM the 7, 8?

The complying with equation can be supplied to express the relation between GCF and also LCM of 7 and 8, i.e. GCF × LCM = 7 × 8.

If the LCM of 8 and also 7 is 56, find its GCF.

LCM(8, 7) × GCF(8, 7) = 8 × 7Since the LCM of 8 and 7 = 56⇒ 56 × GCF(8, 7) = 56Therefore, the GCF (greatest usual factor) = 56/56 = 1.

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How to find the LCM the 7 and 8 by prime Factorization?

To discover the LCM the 7 and also 8 utilizing prime factorization, us will find the element factors, (7 = 7) and (8 = 2 × 2 × 2). LCM that 7 and 8 is the product that prime determinants raised to your respective greatest exponent amongst the number 7 and 8.⇒ LCM that 7, 8 = 23 × 71 = 56.