What is the Least Common Multiple of 45552 and 45564?

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 45552 and 45564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45552 and 45564, than apply into the LCM equation.

GCF(45552,45564) = 12
LCM(45552,45564) = ( 45552 × 45564) / 12
LCM(45552,45564) = 2075531328 / 12
LCM(45552,45564) = 172960944

Least Common Multiple (LCM) of 45552 and 45564 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45552 and 45564. First we will calculate the prime factors of 45552 and 45564.

Prime Factorization of 45552

Prime Factorization of 45564

Now multiplying the highest exponent prime factors to calculate the LCM of 45552 and 45564.

LCM(45552,45564) = 2⁴ × 3¹ × 13¹ × 73¹ × 3797¹
LCM(45552,45564) = 172960944