What is the Least Common Multiple of 75180 and 75196?

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 75180 and 75196 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75180 and 75196, than apply into the LCM equation.

GCF(75180,75196) = 4
LCM(75180,75196) = ( 75180 × 75196) / 4
LCM(75180,75196) = 5653235280 / 4
LCM(75180,75196) = 1413308820

Least Common Multiple (LCM) of 75180 and 75196 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75180 and 75196. First we will calculate the prime factors of 75180 and 75196.

Prime Factorization of 75180

Prime Factorization of 75196

Now multiplying the highest exponent prime factors to calculate the LCM of 75180 and 75196.

LCM(75180,75196) = 2² × 3¹ × 5¹ × 7¹ × 179¹ × 11¹ × 1709¹
LCM(75180,75196) = 1413308820