# What is the Least Common Multiple of 40 and 48?

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 40 and 48 is 240.

LCM(40,48) = 240

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## Least Common Multiple of 40 and 48 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 48, than apply into the LCM equation.

GCF(40,48) = 8
LCM(40,48) = ( 40 × 48) / 8
LCM(40,48) = 1920 / 8
LCM(40,48) = 240

## Least Common Multiple (LCM) of 40 and 48 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 48. First we will calculate the prime factors of 40 and 48.

### Prime Factorization of 40

Prime factors of 40 are 2, 5. Prime factorization of 40 in exponential form is:

40 = 23 × 51

### Prime Factorization of 48

Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:

48 = 24 × 31

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 48.

LCM(40,48) = 24 × 51 × 31
LCM(40,48) = 240