LCM of 12, 15 and 18 - Methods and Solved Examples

Last Updated on Jun 10, 2024
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The Least Common Multiple (LCM) of 12, 15, and 18 is 180. This concept is fundamental to the understanding of numerous mathematical problems. The article Prime Factorisation and Division Method for LCM and HCF provides comprehensive knowledge on how to calculate the least common multiple and highest common factors of any set of numbers. This article will guide you on how to accurately calculate the LCM of 12, 15, and 18.

Understanding the LCM of 12, 15, and 18

The Least Common Multiple of 12, 15, and 18 is 180.

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Methods to Calculate LCM of 12, 15, and 18

The LCM of 12, 15, and 18 can be found using the following methods:

  • Prime Factorisation
  • Division method
  • Listing the Multiples

Calculating LCM of 12, 15, and 18 Using Prime Factorisation

The prime factorisation method involves expressing the given numbers as the product of prime factors. Thus, the numbers 12, 15, and 18 can be expressed as:

12 = 2 × 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

Therefore, LCM (12, 15, 18) = 2 × 2 × 3 × 3 × 5 = 180

Calculating LCM of 12, 15, and 18 Using Division Method

The division method involves dividing the numbers 12, 15, and 18 by a common prime number until the remainder is a prime number or one. The product of these divisors is the least common multiple of 12, 15, and 18.

2 12 15 18
2 6 15 9
3 3 15 9
3 1 5 3
5 1 5 1
x 1 1 1

No more division is possible.

Hence, LCM (12, 15, 18) = 2 × 2 × 3 × 3 × 5 = 180

Calculating LCM of 12, 15, and 18 by Listing Multiples

This method involves listing the multiples of 12, 15, and 18 to find the least common multiple. The multiples of 12, 15, and 18 are shown below.

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,……….., 156, 168, 180, ……..

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, ………..

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, …………

Therefore, LCM (12, 15, 18) = 180

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Frequently Asked Questions

The LCM of 12, 15 and 18 is 180.

No. The LCM of 12, 15 and 18 is 180 and the HCF of 12, 15 and 18 is 3.

The methods used to find the LCM of 12, 15 and 18 are as follows: Prime Factorisation, Division method, Listing the Multiples.

To find the LCM by prime factorisation, we express the numbers as the product of prime factors 12 = 2 × 2 × 3, 15 = 3 × 5, 18 = 2 × 3 × 3. LCM (12, 15, 18) = 2 × 2 × 3 × 3 × 5 = 180.

No. The LCM of 12, 15 and 18 is 180.

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