What is the Least Common Multiple of 75168 and 75186?

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 75186 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 75186, than apply into the LCM equation.

GCF(75168,75186) = 18
LCM(75168,75186) = ( 75168 × 75186) / 18
LCM(75168,75186) = 5651581248 / 18
LCM(75168,75186) = 313976736

Least Common Multiple (LCM) of 75168 and 75186 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75168 and 75186. First we will calculate the prime factors of 75168 and 75186.

Prime Factorization of 75168

Prime Factorization of 75186

Now multiplying the highest exponent prime factors to calculate the LCM of 75168 and 75186.

LCM(75168,75186) = 2⁵ × 3⁴ × 29¹ × 4177¹
LCM(75168,75186) = 313976736