brightchamps-logo
hamburger
Login

open_icon Table Of Contents

LIGHT_BULB_MATHS_BLOG
scholar-purple-hat108 Learners

Last updated on September 17th, 2024

maths_whiteboard

LCM of 3 and 12

maths_mascot
Foundation
Intermediate
Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 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.

GREEN_BACKGROUND_HEADING_MASCOT

What is the LCM of 3 and 12?

The LCM of 3 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.

GREEN_BACKGROUND_HEADING_MASCOT

How to Find the LCM of 3 and 12?

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

GREEN_BACKGROUND_HEADING_MASCOT

LCM of 3 and 12 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 3 = 3, 6, 9, 12, 15, 18, …

  — Multiples of 12 = 12, 24, 36, …

  1. Ascertain the smallest multiple from the listed multiples:

  — The smallest common multiple is 12.

Thus, LCM(3, 12) = 12

GREEN_BACKGROUND_HEADING_MASCOT

LCM of 3 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. Find the prime factors of the numbers:

  — Prime factorization of 3 = 3

  — Prime factorization of 12 = 2 × 2 × 3

  1. Take the highest powers of each prime factor:

  — Highest power of 2 = 2²

  — Highest power of 3 = 3¹

  1.  Multiply the highest powers to get the LCM:

  —LCM(3, 12) = 2² × 3 = 12.

GREEN_BACKGROUND_HEADING_MASCOT

LCM of 3 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; 3, 12 and divide by common prime factors and multiply the divisors.

  — 2 × 2 × 3 = 12

Thus, LCM(3, 12) = 12

GREEN_BACKGROUND_HEADING_MASCOT

Important glossaries for the LCM of 3 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 of a whole.