What is the Least Common Multiple of 45648 and 45660?

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 45648 and 45660 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45648 and 45660, than apply into the LCM equation.

GCF(45648,45660) = 12
LCM(45648,45660) = ( 45648 × 45660) / 12
LCM(45648,45660) = 2084287680 / 12
LCM(45648,45660) = 173690640

Least Common Multiple (LCM) of 45648 and 45660 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45648 and 45660. First we will calculate the prime factors of 45648 and 45660.

Prime Factorization of 45648

Prime Factorization of 45660

Now multiplying the highest exponent prime factors to calculate the LCM of 45648 and 45660.

LCM(45648,45660) = 2⁴ × 3² × 317¹ × 5¹ × 761¹
LCM(45648,45660) = 173690640