What is the Least Common Multiple of 72405 and 72414?

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 72405 and 72414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72405 and 72414, than apply into the LCM equation.

GCF(72405,72414) = 9
LCM(72405,72414) = ( 72405 × 72414) / 9
LCM(72405,72414) = 5243135670 / 9
LCM(72405,72414) = 582570630

Least Common Multiple (LCM) of 72405 and 72414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72405 and 72414. First we will calculate the prime factors of 72405 and 72414.

Prime Factorization of 72405

Prime Factorization of 72414

Now multiplying the highest exponent prime factors to calculate the LCM of 72405 and 72414.

LCM(72405,72414) = 3⁵ × 5¹ × 1609¹ × 2¹ × 149¹
LCM(72405,72414) = 582570630