How to Calculate HCF and LCM of Fractions?

Last Updated : 14 Jan, 2026

To calculate the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of fractions, find the HCF and LCM of their numerators and denominators separately and then use the following formulas for further calculation.

HCF of Fractions

The formula for the HCF of fractions is:

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

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

Solution:

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

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

LCM of Fractions

The formula for the LCM of fractions is:

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

Conditions:

  • All fractions are in their lowest (simplest) form.
  • Numerators and denominators are pairwise co-prime (no common factor between any numerator and any denominator).

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 HCF and LCM of Fractions

Example 1: Calculate the HCF of the fractions 3/8, 9/16, and 6/32.

Solution:

  • HCF(3, 9, 6) = 3
  • Numerators: 3, 9, 6
  • Denominators: 8, 16, 32
    • LCM(8, 16, 32) = 32

HCF of 3/8, 9/16, and 6/32​ = HCF(3, 9, 6)/LCM(8, 16, 32) = 3/32

Example 2: Calculate the LCM of the fractions 3/8, 9/16, and 6/32.

Solution:

  • LCM(3, 9, 6) = 18
  • Numerators: 3, 9, 6
  • Denominators: 8, 16, 32
    • HCF(8, 16, 32) = 8

LCM of 3/8, 9/16, and 6/32​ = LCM(3, 9, 6)/HCF(8, 16, 32) = 18/8 = 9/4

Example 3: Find the HCF and LCM of the fractions: 7/9, and 14/15

Solution:

  • HCF(7, 14) = 7
  • LCM(7, 14) = 14
  • Numerators: 7, 14
  • Denominators: 9, 15
    • HCF(9, 15) = 3
    • LCM(9, 15) = 45

Using formulas for HCF and LCM of fractions we get,

  • HCF of 7/9, and 14/15 = HCF( 7, 14)/LCM(9, 15) = 7/45
  • LCM of 7/9, and 14/15 = LCM(7, 14) /HCF(9, 15) = 14/3

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Practice Questions on HCF and LCM of Fractions

Question 1.Find the HCF and LCM of the following fractions:4/15, 8/25

Question 2. Determine the HCF and LCM of these fractions: 9/20, 27/40, 18/50

Question 3. Calculate the HCF and LCM of the given fractions:5/12, 5/9, 15/24

Question 4. Find the HCF and LCM of the following fractions:2/7, 8/21, 5/7

Question 5. Determine the HCF and LCM of these fractions: 3/8, 12/16, 18/24

Answer Key:

  1. HCF = 4/75 and LCM = 8/3
  2. HCF = 9/200, and LCM = 27/10
  3. HCF = 5/72, and LCM = 5
  4. HCF = 2/42​, and LCM = 40/7
  5. HCF = 3/24​, and LCM = 9/2
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