# What is the Least Common Multiple of 10 and 24?

*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 10 and 24 is **120**.

LCM(10,24) = 120

## Least Common Multiple of 10 and 24 with GCF Formula

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

We need to calculate greatest common factor 10 and 24, than apply into the LCM equation.

GCF(10,24) = 2

LCM(10,24) = ( 10 × 24) / 2

LCM(10,24) = 240 / 2

LCM(10,24) = 120

## Least Common Multiple (LCM) of 10 and 24 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 24. First we will calculate the **prime factors of 10 and 24**.

### Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of **10** in exponential form is:

10 = 2^{1} × 5^{1}

### Prime Factorization of 24

Prime factors of 24 are 2, 3. Prime factorization of **24** in exponential form is:

24 = 2^{3} × 3^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 10 and 24**.

LCM(10,24) = 2^{3} × 5^{1} × 3^{1}

LCM(10,24) = 120