What is the Least Common Multiple of 5649 and 5664?

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 5649 and 5664 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5649 and 5664, than apply into the LCM equation.

GCF(5649,5664) = 3
LCM(5649,5664) = ( 5649 × 5664) / 3
LCM(5649,5664) = 31995936 / 3
LCM(5649,5664) = 10665312

Least Common Multiple (LCM) of 5649 and 5664 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5649 and 5664. First we will calculate the prime factors of 5649 and 5664.

Prime Factorization of 5649

Prime Factorization of 5664

Now multiplying the highest exponent prime factors to calculate the LCM of 5649 and 5664.

LCM(5649,5664) = 3¹ × 7¹ × 269¹ × 2⁵ × 59¹
LCM(5649,5664) = 10665312