What is the Least Common Multiple of 74988 and 75000?

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 74988 and 75000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74988 and 75000, than apply into the LCM equation.

GCF(74988,75000) = 12
LCM(74988,75000) = ( 74988 × 75000) / 12
LCM(74988,75000) = 5624100000 / 12
LCM(74988,75000) = 468675000

Least Common Multiple (LCM) of 74988 and 75000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74988 and 75000. First we will calculate the prime factors of 74988 and 75000.

Prime Factorization of 74988

Prime Factorization of 75000

Now multiplying the highest exponent prime factors to calculate the LCM of 74988 and 75000.

LCM(74988,75000) = 2³ × 3² × 2083¹ × 5⁵
LCM(74988,75000) = 468675000