what is the least common multiple of 12 and 18

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LCM of 12 and 18

LCM of 12 and 18 is the smallest quantity amongst all widespread multiples of 12 and 18. The primary few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 generally used strategies to seek out LCM of 12 and 18 – by itemizing multiples, by prime factorization, and by division technique.

1. LCM of 12 and 18 2. Listing of Strategies 3. Solved Examples 4. FAQs

Reply: LCM of 12 and 18 is 36.

Studying: what’s the least widespread a number of of 12 and 18

LCM of 12 and 18

Rationalization:

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The LCM of two non-zero integers, x(12) and y(18), is the smallest optimistic integer m(36) that’s divisible by each x(12) and y(18) with none the rest.

Let’s take a look at the completely different strategies for locating the LCM of 12 and 18.

  • By Division Methodology
  • By Prime Factorization Methodology
  • By Itemizing Multiples

LCM of 12 and 18 by Division Methodology

LCM of 12 and 18 by Division Method

To calculate the LCM of 12 and 18 by the division technique, we’ll divide the numbers(12, 18) by their prime elements (ideally widespread). The product of those divisors offers the LCM of 12 and 18.

  • Step 1: Discover the prime quantity that may be a issue of a minimum of one of many numbers, 12 and 18. Write this prime quantity(2) on the left of the given numbers(12 and 18), separated as per the ladder association.
  • Step 2: If any of the given numbers (12, 18) is a a number of of two, divide it by 2 and write the quotient under it. Carry down any quantity that’s not invisible by the prime quantity.
  • Step 3: Proceed the steps till solely 1s are left within the final row.

The LCM of 12 and 18 is the product of all prime numbers on the left, ie LCM(12, 18) by division technique = 2 × 2 × 3 × 3 = 36.

LCM of 12 and 18 by Prime Factorization

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Prime factorization of 12 and 18 is (2 × 2 × 3) = 22 × 31 and (2 × 3 × 3) = 21 × 32 respectively. The LCM of 12 and 18 might be obtained by multiplying prime elements raised to their respective highest energy, ie 22 × 32 = 36. Therefore, the LCM of 12 and 18 by prime factorization is 36.

LCM of 12 and 18 by Itemizing Multiples

LCM of 12 and 18 by Listing Multiples Method

To calculate the LCM of 12 and 18 by itemizing out the widespread multiples, we will comply with the given under steps:

  • Step 1: Listing a couple of multiples of 12 (12, 24, 36, 48, 60, 72, 84, . . . . ) and 18 (18, 36, 54, 72, . . . . . )
  • Step 2: The widespread multiples from the multiples of 12 and 18 are 36, 72, . . .
  • Step 3: The smallest widespread a number of of 12 and 18 is 36.

∴ The least widespread a number of of 12 and 18 = 36.

☛ Additionally Examine:

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  • LCM of 15 and 27 – 135
  • LCM of 15 and 25 – 75
  • LCM of 15 and 24 – 120
  • LCM of 15 and 21 – 105
  • LCM of 15 and 20 – 60
  • LCM of 15 and 18 – 90
  • LCM of 15 and 17 – 255

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