The least common denominator for 1 / 2 , 3 / 5 and 9 / 15

Step-by-step explanation:

This is very simple. Make sure that the three fractions are simplified to their lowest equivalent terms (which is popularly referred to as lowest term).

Then, you can use this formula.

Lcm of Fractions = Lcm of Numerators / Hcf of Denominators.

Consider the example below.

Find the Lcm of 5/6 , 3/9, and 4/10.

SOLUTION:

By Simplifying the fractions to its simplest form (i.e reduction to its lowest equivalent term).

Lcm of 5/6, 3/9 & 4/10 = Lcm of 5/6, 1/3 & 2/5

Using the formula,

Lcm of 5/6, 1/3, & 2/5 = Lcm of 5, 1 & 2 / Hcf of 6, 3 & 5

= 10/1

= 10.

To check if this answer is true, we would have to find the Hcf (a.k.a GCD or GCF) of the fractions using the formula below.

Hcf of Fractions = Hcf of Numerators / Lcm of Denominators

Hcf of 5/6, 1/3 & 2/5 = Hcf of 5, 1 & 2 / Lcm of 6, 3

& 5

= 1/30.

Finally, when we divide 5/6, 3/9 & 4/10 each by their Hcf , the result for each fractions is an integer which means factorization is possible, any other number that can factorize these fractions will not be higher or greater than 1/30. The word highest and factor or divisor common to the given nos or fractions brought about the name HCF (a.k.a GCD or GCF).

Also, when the Lcm of the fractions i.e 10 is divided each by 5/6, 3/9 & 4/10, it gives the an integer for each fractions. Remember that when finding Lcm using multiple method, the multiplier is always an integer.

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