LCM of Fractions With Examples and FAQ – Mindspark

How to Find LCM of Fractions

LCM is the smallest common multiple of the given numbers. HCF is the largest number, which divides the given numbers completely. 

LCM of fractions will be the smallest fraction that is a multiple of the given fractions. To calculate it, we use the formula given below – 

LCM of fractions = (LCM of all the numerators)/(HCF of all the denominators)

Let us understand this using a mathematical problem. 

Example- Find the LCM of \frac{2}{3} \text{ and } \frac{3}{5}.

As we know the formula,

LCM of the fractions = (LCM of all the numerators)/(HCF of all the denominators)

Here the numerators are 2 and 3; denominators are 3 and 5.

LCM of numerators (2 and 3) = 6

HCF of denominators (3 and 5) = 1

Now, we will put these values in the formula of fractions.

We get, LCM of \frac{2}{3} \text{ and } \frac{3}{5}= (LCM of 2, 3)/(HCF of 3, 5)

So, LCM of \frac{2}{3} \text{ and } \frac{3}{5} = \frac{6}{1} = 6

Similarly, we can find LCM of three or more fractions also. Let us see an example.

Example- Find the LCM of \frac{1}{2} ,\frac{5}{6}\text{ and } \frac {7}{8}.

Now we have three numerators – 1, 5, and 7

And also three denominators – 2, 6, and 8

LCM of numerators (1, 5, 7) = 35

HCF of denominators (2, 6, 8) = 2

Now using the formula of LCM of fractions –

LCM of \frac{1}{2},\frac{5}{6}\text{ and }\frac{7}{8} = (LCM of 1, 5, 7) / (HCF of 2, 6, 8)

So, LCM of \frac{1}{2},\frac{5}{6}\text{ and }\frac{7}{8} =\frac{35}{2}=17\frac{1}{2}

Examples

1. What is the LCM of \frac{3}{4} \text{ and }\frac{1}{3}?

LCM of the fractions = (LCM of all the numerators)/(HCF of all the denominators)

Here the numerators are 3 and 1.

The LCM of 3 and 1 will be 3.

The denominators are 4 and 3

The HCF of 4 and 3 will be 1.

So,

LCM of \frac{3}{4}\text{ and } \frac{1}{3}= (LCM of 3, 1) / (HCF of 4, 3)

Therefore, LCM of \frac{3}{4} \text{ and }\frac{1}{3}= \frac{3}{1} = 3

2. What is the LCM of \frac{1}{2},\frac{5}{6}\text{ and }\frac{15}{8}?

LCM of fractions = (LCM of all the numerators)/(HCF of all the denominators)

Here the numerators are 1, 5 and 15.

LCM of 1, 5 and 15 will be 15.

The denominators are 2, 6 and 8

HCF of 2, 6 and 8 will be 2.

So,

LCM of \frac{1}{2},\frac{5}{6}\text{ and }\frac{15}{8}

= (LCM of 1, 5, 15) / (HCF of 2, 6, 8)

Therefore, LCM of \frac{1}{2},\frac{5}{6}\text{ and }\frac{15}{8}

= \frac{15}{2}=7\frac{1}{2}