Find the LCM of 12 and 27 - Complete Guide with Methods and Examples

Last Updated on Jun 07, 2024
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The Least Common Multiple (LCM) of 12 and 27 is 108. LCM is the smallest number that is exactly divisible by both numbers. The LCM of 12 and 27 can be calculated using various methods such as prime factorisation, division, and listing the multiples.

Also read: What is the Least Common Multiple?

Understanding the LCM of 12 and 27

The LCM of 12 and 27 is 108. This is the smallest positive integer that is divisible by both 12 and 27 without leaving a remainder.

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Methods to Find the LCM of 12 and 27

The LCM of 12 and 27 can be calculated using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

Using Prime Factorisation to Find the LCM of 12 and 27

The prime factorisation of 12 is 2² x 3¹, and for 27, it is 3³. Therefore, the LCM of 12 and 27 is 108.

Using Division Method to Find the LCM of 12 and 27

By dividing the numbers 12 and 27 by their common prime factors and then multiplying the divisors, we can find the LCM of 12 and 27.

The LCM of 12 and 27 is 108.

Using the Listing Multiples Method to Find the LCM of 12 and 27

By listing the multiples of 12 and 27, we can find the LCM. The LCM of 12 and 27 is the smallest common multiple of both numbers, which is 108.

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Examples of LCM of 12 and 27

Here's an example: Given that the LCM and GCD of two numbers are 108 and 3 respectively, and one of the numbers is 27, we can find the other number by using the formula GCD x LCM = product of the two numbers. Substituting the given values, we find that the other number is 12.

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Frequently Asked Questions

The GCF for 12 and 27 is 3.

The LCM of 12 and 27 is 108.

The relation between GCF and LCM of 12 and 27 is LCM x GCF = 12 x 27 = 324.

The LCM of 12 and 27 is 108.

The methods we can use to get the LCM of 12 and 27 are division, listing multiples and prime factorisation.

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