What is the Least Common Multiple of 75210 and 75225?

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 75210 and 75225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75210 and 75225, than apply into the LCM equation.

GCF(75210,75225) = 15
LCM(75210,75225) = ( 75210 × 75225) / 15
LCM(75210,75225) = 5657672250 / 15
LCM(75210,75225) = 377178150

Least Common Multiple (LCM) of 75210 and 75225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75210 and 75225. First we will calculate the prime factors of 75210 and 75225.

Prime Factorization of 75210

Prime Factorization of 75225

Now multiplying the highest exponent prime factors to calculate the LCM of 75210 and 75225.

LCM(75210,75225) = 2¹ × 3¹ × 5² × 23¹ × 109¹ × 17¹ × 59¹
LCM(75210,75225) = 377178150