What is the Least Common Multiple of 17649 and 17664?

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 17649 and 17664 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17649 and 17664, than apply into the LCM equation.

GCF(17649,17664) = 3
LCM(17649,17664) = ( 17649 × 17664) / 3
LCM(17649,17664) = 311751936 / 3
LCM(17649,17664) = 103917312

Least Common Multiple (LCM) of 17649 and 17664 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17649 and 17664. First we will calculate the prime factors of 17649 and 17664.

Prime Factorization of 17649

Prime Factorization of 17664

Now multiplying the highest exponent prime factors to calculate the LCM of 17649 and 17664.

LCM(17649,17664) = 3² × 37¹ × 53¹ × 2⁸ × 23¹
LCM(17649,17664) = 103917312