What is the Least Common Multiple of 45312 and 45321?

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 45312 and 45321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45312 and 45321, than apply into the LCM equation.

GCF(45312,45321) = 3
LCM(45312,45321) = ( 45312 × 45321) / 3
LCM(45312,45321) = 2053585152 / 3
LCM(45312,45321) = 684528384

Least Common Multiple (LCM) of 45312 and 45321 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45312 and 45321. First we will calculate the prime factors of 45312 and 45321.

Prime Factorization of 45312

Prime Factorization of 45321

Now multiplying the highest exponent prime factors to calculate the LCM of 45312 and 45321.

LCM(45312,45321) = 2⁸ × 3¹ × 59¹ × 15107¹
LCM(45312,45321) = 684528384