What is the Least Common Multiple of 45492 and 45504?

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 45492 and 45504 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45492 and 45504, than apply into the LCM equation.

GCF(45492,45504) = 12
LCM(45492,45504) = ( 45492 × 45504) / 12
LCM(45492,45504) = 2070067968 / 12
LCM(45492,45504) = 172505664

Least Common Multiple (LCM) of 45492 and 45504 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45492 and 45504. First we will calculate the prime factors of 45492 and 45504.

Prime Factorization of 45492

Prime Factorization of 45504

Now multiplying the highest exponent prime factors to calculate the LCM of 45492 and 45504.

LCM(45492,45504) = 2⁶ × 3² × 17¹ × 223¹ × 79¹
LCM(45492,45504) = 172505664