What is the Least Common Multiple of 96000 and 96015?

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 96015 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 96015, than apply into the LCM equation.

GCF(96000,96015) = 15
LCM(96000,96015) = ( 96000 × 96015) / 15
LCM(96000,96015) = 9217440000 / 15
LCM(96000,96015) = 614496000

Least Common Multiple (LCM) of 96000 and 96015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 96000 and 96015. First we will calculate the prime factors of 96000 and 96015.

Prime Factorization of 96000

Prime Factorization of 96015

Now multiplying the highest exponent prime factors to calculate the LCM of 96000 and 96015.

LCM(96000,96015) = 2⁸ × 3¹ × 5³ × 37¹ × 173¹
LCM(96000,96015) = 614496000