Math Egypt

Finding Like Denominators Using the L.C.M

In this lesson, we will learn how to change two fractions with unlike denominators into fractions with like denominators using the L.C.M (Least Common Multiple).

Step 1: Factorize the Denominators

Example: $ \frac{3}{8} $ and $ \frac{5}{12} $

$8 = 2 \times 2 \times 2$
$12 = 2 \times 2 \times 3$

Step 2: Find the L.C.M

Take each prime factor the greatest number of times it appears:

$L.C.M = 2 \times 2 \times 2 \times 3 = 24$

Step 3: Convert Each Fraction

$ \frac{3}{8} = \frac{9}{24} $
$ \frac{5}{12} = \frac{10}{24} $

Now the two fractions have like denominators: $ \frac{9}{24} $ and $ \frac{10}{24} $

Practice

Change each pair into like denominators using the L.C.M:

a) $ \frac{3}{8} $ , $ \frac{5}{10} $
b) $ \frac{7}{10} $ , $ \frac{11}{15} $
c) $ \frac{5}{6} $ , $ \frac{2}{3} $