What is the Least Common Multiple for 8 and 12? – Clarification and More

What is the Least Common Multiple for 8 and 12

What is the Least Common Multiple for 8 and 12 – The LCM is the method to find the minimum possible multiple of two or more numbers.

The LCM stands for Least common multiple. LCM of 3 numbers is divisible by both numbers.

The different methods for discovering the LCM of 8 and 12

• Prime Factorization Method
• Division Method
• Listing Multiples

LCM of 8 and 12

• Here Least Common Multiple of 8 and 12 is the smallest number among all common multiples 8 and 12.
• However, the first few multiples of 8 and 12 are (8, 16, 24, 32, . . . ) and (12, 24, 36, 48, 60, . . . ) respectively.
• Here are three commonly used methods to find LCM of 8 and 12 – by division, prime factorization, and listing multiples.

The LCM for 8 and 12?

Reaction: LCM of 8 and 12 is 24.

Clarification:

The LCM of two nonzero integers, x(8) and y(12), is the most miniature positive integer m(24) that is divisible by x(8) and y(12) with no remainder.

LCM of 8 and 12 via Prime Factorization

Here prime factorization of 8 and 12 is (2 × 2 × 2) = 23 and (2 × 2 × 3) = 22 × 31 respectively. The LCM of 8 and 12 can be obtained by multiplying prime factors raised to their own highest power. For example, 23 × 31 = 24.

However, the LCM of 8 and 12 through prime factorization is 24.

LCM of 8 and 12 via Division Method

In calculating the LCM of 8 and 12 by the division method, we will divide the numbers (8, 12) by their prime (preferably common) factors. Here the product of these divisors gives the LCM of 8 and 12.

1: Discovery the smallest prime number that is a factor of at least one of the numbers, 8 and 12. Write this prime number (2) to the left of the numbers (8 and 12). Spaced according to the layout on a ladder.

2: If slightly of the given numbers (8, 12) is a multiple of 2, divide by 2 and write the quotient below. Reduce any number that is not divisible by the prime number.

3: Continue the steps until there is only 1 left in the last row.

Here LCM of 8 and 12 is the creation of all the primes on the left, LCM(8, 12) by division = 2 × 2 × 2 × 3 = 24.

LCM of 8 and 12 via Listing Multiples

Here to calculate the LCM of 8 and 12 by listing the common multiples, we can follow these steps:

1: List some multiples of 8 (8, 16, 24, 32, …) and 12 (12, 24, 36, 48, 60, …)

2: The common multiples of the multiples of 8 and 12 are 24, 48,

3: The least common multiple of 8 and 12 is 24.

Here The LCM of 8 and 12 = 24.

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