What is the Least Common Multiple of 27664 and 27680?

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 27664 and 27680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27664 and 27680, than apply into the LCM equation.

GCF(27664,27680) = 16
LCM(27664,27680) = ( 27664 × 27680) / 16
LCM(27664,27680) = 765739520 / 16
LCM(27664,27680) = 47858720

Least Common Multiple (LCM) of 27664 and 27680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27664 and 27680. First we will calculate the prime factors of 27664 and 27680.

Prime Factorization of 27664

Prime Factorization of 27680

Now multiplying the highest exponent prime factors to calculate the LCM of 27664 and 27680.

LCM(27664,27680) = 2⁵ × 7¹ × 13¹ × 19¹ × 5¹ × 173¹
LCM(27664,27680) = 47858720