What is the Least Common Multiple of 96120 and 96128?

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 96120 and 96128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96120 and 96128, than apply into the LCM equation.

GCF(96120,96128) = 8
LCM(96120,96128) = ( 96120 × 96128) / 8
LCM(96120,96128) = 9239823360 / 8
LCM(96120,96128) = 1154977920

Least Common Multiple (LCM) of 96120 and 96128 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 96120 and 96128. First we will calculate the prime factors of 96120 and 96128.

Prime Factorization of 96120

Prime Factorization of 96128

Now multiplying the highest exponent prime factors to calculate the LCM of 96120 and 96128.

LCM(96120,96128) = 2⁷ × 3³ × 5¹ × 89¹ × 751¹
LCM(96120,96128) = 1154977920