What is the Least Common Multiple of 45015 and 45024?

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 45015 and 45024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45015 and 45024, than apply into the LCM equation.

GCF(45015,45024) = 3
LCM(45015,45024) = ( 45015 × 45024) / 3
LCM(45015,45024) = 2026755360 / 3
LCM(45015,45024) = 675585120

Least Common Multiple (LCM) of 45015 and 45024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45015 and 45024. First we will calculate the prime factors of 45015 and 45024.

Prime Factorization of 45015

Prime Factorization of 45024

Now multiplying the highest exponent prime factors to calculate the LCM of 45015 and 45024.

LCM(45015,45024) = 3¹ × 5¹ × 3001¹ × 2⁵ × 7¹ × 67¹
LCM(45015,45024) = 675585120