What is the Least Common Multiple of 5640 and 5649?

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 5640 and 5649 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5640 and 5649, than apply into the LCM equation.

GCF(5640,5649) = 3
LCM(5640,5649) = ( 5640 × 5649) / 3
LCM(5640,5649) = 31860360 / 3
LCM(5640,5649) = 10620120

Least Common Multiple (LCM) of 5640 and 5649 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5640 and 5649. First we will calculate the prime factors of 5640 and 5649.

Prime Factorization of 5640

Prime Factorization of 5649

Now multiplying the highest exponent prime factors to calculate the LCM of 5640 and 5649.

LCM(5640,5649) = 2³ × 3¹ × 5¹ × 47¹ × 7¹ × 269¹
LCM(5640,5649) = 10620120