What is the Least Common Multiple of 5664 and 5670?

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 5664 and 5670 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5664 and 5670, than apply into the LCM equation.

GCF(5664,5670) = 6
LCM(5664,5670) = ( 5664 × 5670) / 6
LCM(5664,5670) = 32114880 / 6
LCM(5664,5670) = 5352480

Least Common Multiple (LCM) of 5664 and 5670 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5664 and 5670. First we will calculate the prime factors of 5664 and 5670.

Prime Factorization of 5664

Prime Factorization of 5670

Now multiplying the highest exponent prime factors to calculate the LCM of 5664 and 5670.

LCM(5664,5670) = 2⁵ × 3⁴ × 59¹ × 5¹ × 7¹
LCM(5664,5670) = 5352480