What is the Least Common Multiple of 84 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 84 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 84 and 96, than apply into the LCM equation.

GCF(84,96) = 12
LCM(84,96) = ( 84 × 96) / 12
LCM(84,96) = 8064 / 12
LCM(84,96) = 672

Least Common Multiple (LCM) of 84 and 96 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 96. First we will calculate the prime factors of 84 and 96.

Prime Factorization of 84

Prime Factorization of 96

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 96.

LCM(84,96) = 2⁵ × 3¹ × 7¹
LCM(84,96) = 672