What is the Least Common Multiple of 45888 and 45900?

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 45888 and 45900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45888 and 45900, than apply into the LCM equation.

GCF(45888,45900) = 12
LCM(45888,45900) = ( 45888 × 45900) / 12
LCM(45888,45900) = 2106259200 / 12
LCM(45888,45900) = 175521600

Least Common Multiple (LCM) of 45888 and 45900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45888 and 45900. First we will calculate the prime factors of 45888 and 45900.

Prime Factorization of 45888

Prime Factorization of 45900

Now multiplying the highest exponent prime factors to calculate the LCM of 45888 and 45900.

LCM(45888,45900) = 2⁶ × 3³ × 239¹ × 5² × 17¹
LCM(45888,45900) = 175521600