What is the Least Common Multiple of 27648 and 27657?

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 27648 and 27657 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27648 and 27657, than apply into the LCM equation.

GCF(27648,27657) = 9
LCM(27648,27657) = ( 27648 × 27657) / 9
LCM(27648,27657) = 764660736 / 9
LCM(27648,27657) = 84962304

Least Common Multiple (LCM) of 27648 and 27657 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27648 and 27657. First we will calculate the prime factors of 27648 and 27657.

Prime Factorization of 27648

Prime Factorization of 27657

Now multiplying the highest exponent prime factors to calculate the LCM of 27648 and 27657.

LCM(27648,27657) = 2¹⁰ × 3³ × 7¹ × 439¹
LCM(27648,27657) = 84962304