# What is the Least Common Multiple of 52 and 71?

*Least common multiple* or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 52 and 71 is **3692**.

LCM(52,71) = 3692

## Least Common Multiple of 52 and 71 with GCF Formula

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 52 and 71, than apply into the LCM equation.

GCF(52,71) = 1

LCM(52,71) = ( 52 × 71) / 1

LCM(52,71) = 3692 / 1

LCM(52,71) = 3692

## Least Common Multiple (LCM) of 52 and 71 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 52 and 71. First we will calculate the **prime factors of 52 and 71**.

### Prime Factorization of 52

Prime factors of 52 are 2, 13. Prime factorization of **52** in exponential form is:

52 = 2^{2} × 13^{1}

### Prime Factorization of 71

Prime factors of 71 are 71. Prime factorization of **71** in exponential form is:

71 = 71^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 52 and 71**.

LCM(52,71) = 2^{2} × 13^{1} × 71^{1}

LCM(52,71) = 3692