LCM of Fractions

LCM of fractions is the smallest value either integer or fraction that can be evenly divided by the given fractions.

Note: The LCM of a fraction can either be an integer or a fraction.

Step 1 : Calculate the LCM of the numerators of the given fraction.

Step 2 : Calculate the HCF of the Denominators of the given fraction.

Step 3 : Compute the LCM of the fractions by using the formula given below,

Formula for LCM of Fractions

LCM of fractions = \frac{LCM of Numerators}{HCF of Denominators}

Example: Find the LCM of 2/3 and 4/9​.
Solution:

• Numerators: 2, 4 → LCM(2, 4) = 4
• Denominators: 3, 9 → HCF(3, 9) = 3

LCM of 2/3​ and 4/9​ =LCM( 2, 4)/HCF(3, 9) = 4/3

Solved Example on LCM of Fractions

Example 1: Calculate the HCF of the fractions 3/8, 5/16, and 3/16.
Solution:

Given fractions: 3/8, 5/16, and 3/16

Numerators: 3, 5, 3
Denominators: 8, 16, 16

LCM of Numerators (3, 5, 3) = 15
HCF of Denominators ( 8, 16, 16 ) = 8

LCM of (3/8, 5/16, and 3/16​ ) = LCM(3, 5, 3)/HCF(8, 16, 16) = 15/8

Example 2: Calculate the LCM of the fractions 2/7 and 9/11.
Solution:

Given fractions: 2/7 and 9/11.

Numerators: 2, 9
Denominators: 7, 11

LCM of Numerators (2, 9) = 18

GCD of denominators (7, 11) = 1(both primes)

LCM of ( 2/7 and 9/11 ) = LCM( 2, 9)/GCD(7, 11) = 18/1 = 18