Question

What is the least common denominator of $\dfrac{1}{2},\dfrac{1}{4}$and$\dfrac{3}{8}$?

Answer 1

Hint: We need to calculate the least common denominator of the three fractions given. For this, we first collect the denominators of all the denominators in the fractions. After that we simply calculate the least common multiple of the denominators i.e. we need to find the smallest number that is multiple of all the given numbers.

Complete step by step solution:
A fraction has two parts, numerator and denominator. The numerator is the upper half of the fraction and the denominator resides on the lower part of a fraction. In the given numbers, the denominator of the first fraction $\dfrac{1}{2}$ is 2. The denominator of the second fraction $\dfrac{1}{4}$ is 4. And for the last fraction $\dfrac{3}{8}$ is 8. So we need to find the least common multiple of 2,4 and 8. For this we write the multiples of all the terms one by one and then we find the least common one out of them. So, we write the multiples as follows:
Multiples of 2: 2,4,6,8,10,$\ldots$
Multiples of 4: 4,8,12,16,$\ldots$
Multiples of 8: 8,16,24,32,$\ldots$
We see here that 8 is common in all of the multiples and also it is the least one too. So we can write that the least common denominator of the fractions $\dfrac{1}{2},\dfrac{1}{4}$and$\dfrac{3}{8}$ is 8.

Note: While writing the multiples, take care that you do not write the factors instead of multiples. These terms often get confusing. To write the multiples, simply take the number and write the result obtained by multiplying that number with first ‘n’ natural numbers.