Question

Find the least common denominator. $$\frac{3}{4}, \frac{2}{5}$$

Short answer

The least common denominator is 20.

Step-by-step solution

Identify the Denominators

The denominators for the given fractions \(\frac{3}{4}\) and \(\frac{2}{5}\) are 4 and 5 respectively.

Find Prime Factors of Each Denominator

The prime factors of 4 are 2 and 2. And the prime factors of 5 is 5 itself. So the prime numbers are 2 and 5.

Find the Least Common Multiple (LCM)

To calculate the LCM, you take each prime number the greatest number of times it occurs in either of the two denominators. The prime number 2 occurs twice in 4 and does not occur in 5, so you take it twice. The prime number 5 occurs once in 5 and not in 4, so you take it once. Multiply these: \(2*2*5 = 20\). Therefore, the LCM is 20.