What is the Least Common Multiple of 96000 and 96012?

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 96000 and 96012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96000 and 96012, than apply into the LCM equation.

GCF(96000,96012) = 12
LCM(96000,96012) = ( 96000 × 96012) / 12
LCM(96000,96012) = 9217152000 / 12
LCM(96000,96012) = 768096000

Least Common Multiple (LCM) of 96000 and 96012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 96000 and 96012. First we will calculate the prime factors of 96000 and 96012.

Prime Factorization of 96000

Prime Factorization of 96012

Now multiplying the highest exponent prime factors to calculate the LCM of 96000 and 96012.

LCM(96000,96012) = 2⁸ × 3³ × 5³ × 7¹ × 127¹
LCM(96000,96012) = 768096000