What is the Least Common Multiple of 75000 and 75012?

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 75000 and 75012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75000 and 75012, than apply into the LCM equation.

GCF(75000,75012) = 12
LCM(75000,75012) = ( 75000 × 75012) / 12
LCM(75000,75012) = 5625900000 / 12
LCM(75000,75012) = 468825000

Least Common Multiple (LCM) of 75000 and 75012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75000 and 75012. First we will calculate the prime factors of 75000 and 75012.

Prime Factorization of 75000

Prime Factorization of 75012

Now multiplying the highest exponent prime factors to calculate the LCM of 75000 and 75012.

LCM(75000,75012) = 2³ × 3¹ × 5⁵ × 7¹ × 19¹ × 47¹
LCM(75000,75012) = 468825000