What is the Least Common Multiple of 75168 and 75188?

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 75168 and 75188 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75168 and 75188, than apply into the LCM equation.

GCF(75168,75188) = 4
LCM(75168,75188) = ( 75168 × 75188) / 4
LCM(75168,75188) = 5651731584 / 4
LCM(75168,75188) = 1412932896

Least Common Multiple (LCM) of 75168 and 75188 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75168 and 75188. First we will calculate the prime factors of 75168 and 75188.

Prime Factorization of 75168

Prime Factorization of 75188

Now multiplying the highest exponent prime factors to calculate the LCM of 75168 and 75188.

LCM(75168,75188) = 2⁵ × 3⁴ × 29¹ × 18797¹
LCM(75168,75188) = 1412932896