What is the Least Common Multiple of 75210 and 75230?

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 75230 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 75230, than apply into the LCM equation.

GCF(75210,75230) = 10
LCM(75210,75230) = ( 75210 × 75230) / 10
LCM(75210,75230) = 5658048300 / 10
LCM(75210,75230) = 565804830

Least Common Multiple (LCM) of 75210 and 75230 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75210 and 75230. First we will calculate the prime factors of 75210 and 75230.

Prime Factorization of 75210

Prime Factorization of 75230

Now multiplying the highest exponent prime factors to calculate the LCM of 75210 and 75230.

LCM(75210,75230) = 2¹ × 3¹ × 5¹ × 23¹ × 109¹ × 7523¹
LCM(75210,75230) = 565804830