# What is the Least Common Multiple of 5 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 5 and 24 is 120.

LCM(5,24) = 120

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## Least Common Multiple of 5 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 5 and 24, than apply into the LCM equation.

GCF(5,24) = 1
LCM(5,24) = ( 5 × 24) / 1
LCM(5,24) = 120 / 1
LCM(5,24) = 120

## Least Common Multiple (LCM) of 5 and 24 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 24. First we will calculate the prime factors of 5 and 24.

### Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:

5 = 51

### Prime Factorization of 24

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

24 = 23 × 31

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 24.

LCM(5,24) = 51 × 23 × 31
LCM(5,24) = 120