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LCM of 6 and 9

LCM of 6 and 9 is the smallest quantity amongst all frequent multiples of 6 and 9. The primary few multiples of 6 and 9 are (6, 12, 18, 24, 30, . . . . ) and (9, 18, 27, 36, . . . ) respectively. There are 3 generally used strategies to search out LCM of 6 and 9 – by prime factorization, by division methodology, and by itemizing multiples.

1. LCM of 6 and 9 2. Listing of Strategies 3. Solved Examples 4. FAQs

Reply: LCM of 6 and 9 is eighteen.

Studying: what’s the lcm of 6 and 9

LCM of 6 and 9

Rationalization:

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The LCM of two non-zero integers, x(6) and y(9), is the smallest constructive integer m(18) that’s divisible by each x(6) and y(9) with none the rest.

The strategies to search out the LCM of 6 and 9 are defined under.

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

LCM of 6 and 9 by Division Methodology

LCM of 6 and 9 by Division Method

To calculate the LCM of 6 and 9 by the division methodology, we’ll divide the numbers(6, 9) by their prime components (ideally frequent). The product of those divisors offers the LCM of 6 and 9.

  • Step 1: Discover the prime quantity that may be a issue of at the very least one of many numbers, 6 and 9. Write this prime quantity(2) on the left of the given numbers(6 and 9), separated as per the ladder association.
  • Step 2: If any of the given numbers (6, 9) is a a number of of two, divide it by 2 and write the quotient under it. Convey 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 6 and 9 is the product of all prime numbers on the left, ie LCM(6, 9) by division methodology = 2 × 3 × 3 = 18.

LCM of 6 and 9 by Itemizing Multiples

LCM of 6 and 9 by Listing Multiples Method

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To calculate the LCM of 6 and 9 by itemizing out the frequent multiples, we will observe the given under steps:

  • Step 1: Listing a number of multiples of 6 (6, 12, 18, 24, 30, . . . ) and 9 (9, 18, 27, 36, . . . . . )
  • Step 2: The frequent multiples from the multiples of 6 and 9 are 18, 36, . . .
  • Step 3: The smallest frequent a number of of 6 and 9 is eighteen.

∴ The least frequent a number of of 6 and 9 = 18.

LCM of 6 and 9 by Prime Factorization

Prime factorization of 6 and 9 is (2 × 3) = 21 × 31 and (3 × 3) = 32 respectively. The LCM of 6 and 9 will be obtained by multiplying prime components raised to their respective highest energy, ie 21 × 32 = 18. Therefore, the LCM of 6 and 9 by prime factorization is eighteen.

☛ Additionally Examine:

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  • LCM of 32 and 64 – 64
  • LCM of 36, 60 and 72 – 360
  • LCM of 15 and 40 – 120
  • LCM of 15, 20 and 25 – 300
  • LCM of 12 and 30 – 60
  • LCM of three, 5 and 11 – 165
  • LCM of 10 and 15 – 30

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