What is the Least Common Multiple of 75200 and 75210?

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 75200 and 75210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75200 and 75210, than apply into the LCM equation.

GCF(75200,75210) = 10
LCM(75200,75210) = ( 75200 × 75210) / 10
LCM(75200,75210) = 5655792000 / 10
LCM(75200,75210) = 565579200

Least Common Multiple (LCM) of 75200 and 75210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75200 and 75210. First we will calculate the prime factors of 75200 and 75210.

Prime Factorization of 75200

Prime Factorization of 75210

Now multiplying the highest exponent prime factors to calculate the LCM of 75200 and 75210.

LCM(75200,75210) = 2⁶ × 5² × 47¹ × 3¹ × 23¹ × 109¹
LCM(75200,75210) = 565579200