LCM

L.C.M. stands for Least Common Multiple.

The L.C.M. of two or more numbers can is the least number obtained that is exactly divisible by all the given number.

Let us understand it from example-

Example- Let 3 numbers be 2, 3, 8.

The least number that would be divided by all the three numbers perfectly ( leaving no remainder) would be 24 (lcm).

There are two methods to find L.C.M of given numbers, they are:

  • Prime factorization method.
  • Division Method.

How to find L.C.M of given numbers by prime factorization method?

Factorization-

Follow the steps below to find L.C.M of given numbers by prime factorization method.

  1. Express the given numbers as product of their prime factors.
  2. Find highest index in all the prime factors of given numbers.
  3. The product of all the prime factors with respective highest indices is the L.C.M of given numbers.

Example:

L.C.M of 14, 42, 36

  1. Express the numbers as product of prime factors.14 =  2*736 = 32 *22
    42 = 2*3*7
  1. The highest index of 2, 3, 7 are 2, 2, 1 respectively
  2. The product of all the prime factors with the respective highest indices

Example.

Ex: L.C.M of 12,98,188

LCM

The product of divisors and remaining numbers = 2*2*3*49*47*= 27636

Hence, the L.C.M of 12,98,188 = 27636

L.C.M of given Fractions

LCM

How to compare fractions by using L.C.M of denominators

 Comparison of fractions

  1. Find L.C.M of the denominators in given fractions
  2. Find the resultant fraction for all the numbers with above L.C.M as denominator
  3. Arrange the corresponding fractions in the order of their numerators of resultant fractions

LCM

To learn more concepts of lcm or hcf visit our site BYJU’S


Practise This Question

Harman told Kushagra that only one line parallel to a given line can be drawn through a point which is not on the line. State whether Harman's statement is true or false.