What is the Least Common Multiple of 75204 and 75220?

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 75204 and 75220 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75204 and 75220, than apply into the LCM equation.

GCF(75204,75220) = 4
LCM(75204,75220) = ( 75204 × 75220) / 4
LCM(75204,75220) = 5656844880 / 4
LCM(75204,75220) = 1414211220

Least Common Multiple (LCM) of 75204 and 75220 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75204 and 75220. First we will calculate the prime factors of 75204 and 75220.

Prime Factorization of 75204

Prime Factorization of 75220

Now multiplying the highest exponent prime factors to calculate the LCM of 75204 and 75220.

LCM(75204,75220) = 2² × 3² × 2089¹ × 5¹ × 3761¹
LCM(75204,75220) = 1414211220