What is the Least Common Multiple of 75888 and 75908?

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 75908 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 75908, than apply into the LCM equation.

GCF(75888,75908) = 4
LCM(75888,75908) = ( 75888 × 75908) / 4
LCM(75888,75908) = 5760506304 / 4
LCM(75888,75908) = 1440126576

Least Common Multiple (LCM) of 75888 and 75908 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75888 and 75908. First we will calculate the prime factors of 75888 and 75908.

Prime Factorization of 75888

Prime Factorization of 75908

Now multiplying the highest exponent prime factors to calculate the LCM of 75888 and 75908.

LCM(75888,75908) = 2⁴ × 3² × 17¹ × 31¹ × 7¹ × 2711¹
LCM(75888,75908) = 1440126576