What is the Least Common Multiple of 75696 and 75708?

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 75696 and 75708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75696 and 75708, than apply into the LCM equation.

GCF(75696,75708) = 12
LCM(75696,75708) = ( 75696 × 75708) / 12
LCM(75696,75708) = 5730792768 / 12
LCM(75696,75708) = 477566064

Least Common Multiple (LCM) of 75696 and 75708 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75696 and 75708. First we will calculate the prime factors of 75696 and 75708.

Prime Factorization of 75696

Prime Factorization of 75708

Now multiplying the highest exponent prime factors to calculate the LCM of 75696 and 75708.

LCM(75696,75708) = 2⁴ × 3³ × 19¹ × 83¹ × 701¹
LCM(75696,75708) = 477566064