What is the Least Common Multiple of 8 and 96?

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 of 8 and 96 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 96, than apply into the LCM equation.

GCF(8,96) = 8
LCM(8,96) = ( 8 × 96) / 8
LCM(8,96) = 768 / 8
LCM(8,96) = 96

Least Common Multiple (LCM) of 8 and 96 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 96. First we will calculate the prime factors of 8 and 96.

Prime Factorization of 8

Prime Factorization of 96

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 96.

LCM(8,96) = 2⁵ × 3¹
LCM(8,96) = 96