What is the Least Common Multiple of 65664 and 65680?

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 65664 and 65680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65664 and 65680, than apply into the LCM equation.

GCF(65664,65680) = 16
LCM(65664,65680) = ( 65664 × 65680) / 16
LCM(65664,65680) = 4312811520 / 16
LCM(65664,65680) = 269550720

Least Common Multiple (LCM) of 65664 and 65680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65664 and 65680. First we will calculate the prime factors of 65664 and 65680.

Prime Factorization of 65664

Prime Factorization of 65680

Now multiplying the highest exponent prime factors to calculate the LCM of 65664 and 65680.

LCM(65664,65680) = 2⁷ × 3³ × 19¹ × 5¹ × 821¹
LCM(65664,65680) = 269550720