How to find the Least Common Multiple(LCM)?


Least Common Multiple (LCM) is a way of finding the smallest common multiple between any two numbers or more. A common multiple is a multiple of two numbers or more. LCM denotes the less common or multiple factors of any two or more given integers.

Example: L.C.M of 16 and 20

Let us consider the multiples of 16 and 20, we get;

16 → 16, 32, 48, 64, 80,…

20 → 20, 40, 60, 80,…,

∴ LCM(16, 20) = 80

Method to finding LCM

There are three important methods by which we can find the LCM of two or more numbers.

Listing the Multiples

The method to find the least common multiple of any given numbers is first to list down the multiples of specific numbers and then find the first common multiple between them.

Example: LCM of 11 and 33

Multiples of 11 = 11, 22, 33, 44, 55, ….

Multiples of 33 = 33, 66, 99, ….

∴ LCM(11 33) = 33

Prime Factorization method

The prime factorization is one of the most common ways of finding LCM.

Example: Calculate the LCM of 30 and 45.

Let us calculate the prime factors of two number

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Multiply each factor the maximum number of times it occurs in either number.

LCM = 2 × 3 × 3 × 5

LCM = 90

Division Method

Finding LCM of two numbers by division method is an easy method. Below are the steps to find the LCM by division method:

  • First, write the numbers, separated by commas
  • Now divide the numbers, by the smallest prime number.
  • If any number is not divisible, then write down that number and proceed further
  • Keep on dividing the row of numbers by prime numbers, unless we get the results as 1 in the complete row
  • Now LCM of the numbers will be equal to the product of all the prime numbers we obtained in the division method

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