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Last updated on November 29th, 2024

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LCM of 7 and 12

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 7 and 12. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

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What is the LCM of 7 and 12?

The LCM of 7 and 12 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.

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How to Find the LCM of 7 and 12?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

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LCM of 7 and 12 using the Listing Multiples Method

The LCM of 7 and 12 can be calculated using the following steps:

Steps:

  1. Write down the multiples of each number

  — Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …

   — Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …

  1. Ascertain the smallest multiple from the listed multiples:

  — The smallest common multiple is 84.

Thus, LCM(7, 12) = 84

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LCM of 7 and 12 using the Prime Factorization Method

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Steps:

  1.  Prime factorization of 7 = 7 (since 7 is prime)
  2. Prime factorization of 12 = 2 × 2 × 3 
  3. Take the highest powers of each prime factor and multiply the highest powers to get the LCM:

—  LCM(7, 12) = 2² × 3 × 7 = 84

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LCM of 7 and 12 using the Division Method

This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.

 

Steps:

— Write the numbers. Divide by common prime factors and multiply the divisors. 

  — 2 × 2 × 3 × 7 = 84

Thus, LCM(7, 12) = 84

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Important glossaries for the LCM of 7 and 12

  • Multiple: A number and any integer multiplied. 
  • Prime Factor: A natural number (other than 1) that has factors that are one and itself.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 
  • Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 
  • Relatively Prime Numbers: Numbers that have no common factors other than 1.
  • Fraction: A representation of a part or a whole
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