What is the Least Common Multiple of 75088 and 75100?

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 75088 and 75100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75088 and 75100, than apply into the LCM equation.

GCF(75088,75100) = 4
LCM(75088,75100) = ( 75088 × 75100) / 4
LCM(75088,75100) = 5639108800 / 4
LCM(75088,75100) = 1409777200

Least Common Multiple (LCM) of 75088 and 75100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75088 and 75100. First we will calculate the prime factors of 75088 and 75100.

Prime Factorization of 75088

Prime Factorization of 75100

Now multiplying the highest exponent prime factors to calculate the LCM of 75088 and 75100.

LCM(75088,75100) = 2⁴ × 13¹ × 19² × 5² × 751¹
LCM(75088,75100) = 1409777200