What is the Least Common Multiple of 75888 and 75900?

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 75888 and 75900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75888 and 75900, than apply into the LCM equation.

GCF(75888,75900) = 12
LCM(75888,75900) = ( 75888 × 75900) / 12
LCM(75888,75900) = 5759899200 / 12
LCM(75888,75900) = 479991600

Least Common Multiple (LCM) of 75888 and 75900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75888 and 75900. First we will calculate the prime factors of 75888 and 75900.

Prime Factorization of 75888

Prime Factorization of 75900

Now multiplying the highest exponent prime factors to calculate the LCM of 75888 and 75900.

LCM(75888,75900) = 2⁴ × 3² × 17¹ × 31¹ × 5² × 11¹ × 23¹
LCM(75888,75900) = 479991600