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scholar-purple-hat110 Learners

Last updated on September 17th, 2024

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LCM of 2 and 5

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Foundation
Intermediate
Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 and 5. 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 2 and 5?

The LCM of 2 and 5 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 2 and 5?

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 2 and 5 using the Listing Multiples Method

The LCM of 2 and 5 can be calculated using the following steps:

Steps:

  1. Write down the multiples of each number

  — Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, …

  — Multiples of 5 = 5, 10, 15, 20, 25, …

  1. Ascertain the smallest multiple from the listed multiples

  — The smallest common multiple is 10.

Thus, LCM(2, 5) = 10

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LCM of 2 and 5 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 the numbers:

  — Prime factorization of 2 = 2

  — Prime factorization of 5 = 5

  1.  Take the highest powers of each prime factor:

  — Highest power of 2 = 2

  — Highest power of 5 = 5

  1.  Multiply the highest powers to get the LCM:

  LCM(2, 5) = 2 × 5 = 10.

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LCM of 2 and 5 using the Division Method

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

Steps:

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

  — 2 × 5 = 10

Thus, LCM(2, 5) = 10

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Important glossaries for the LCM of 2 and 5

  • 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 of a whole.