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Last updated on November 30th, 2024

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LCM of 10 and 15

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 15. 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 10 and 15?

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 10 and 15 using the Listing Multiples Method

The LCM of 10 and 15 can be found ascertained using the following steps

Steps:

  1. Write down the multiples of each number
    • Multiples of 10 = 10, 20, 30, 40,60 …
    • Multiples of 15 = 15,30,45,60,75,…
  2.  Ascertain the smallest multiple from the listed multiples
    • The smallest common multiple is 30. Thus, LCM(10,15) = 30.
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LCM of 10 and 15 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. Find the prime factors of each number: 
    • Prime factorization of 10 =2×5
    • Prime factorization of 15 =5×3
  2. Take the highest powers of each prime factor and multiply the highest powers to get the LCM:
    • LCM(10,15) = 2×3×5= 30
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LCM of 10 and 15 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, and then multiplying the divisors to find the LCM.

Steps:

  1. Write the numbers:

  1. Divide by common prime factors

Multiply the divisors: So, LCM(10,15) = 30

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Important glossaries on the LCM of 10 and 15

  • Multiple: A number multiplied with an integer. 
  • Prime Factor: A natural number (other than 1) whose factors that are one and itself.
  • Prime Factorization: Breaking down a number into its prime factors is called Prime Factorization. 
  • Relatively Prime Numbers: Numbers that have no common factors other than 1.
  • Fraction: A representation of a part of a whole.
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