What is the Least Common Multiple of 23680 and 23696?

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 23680 and 23696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23680 and 23696, than apply into the LCM equation.

GCF(23680,23696) = 16
LCM(23680,23696) = ( 23680 × 23696) / 16
LCM(23680,23696) = 561121280 / 16
LCM(23680,23696) = 35070080

Least Common Multiple (LCM) of 23680 and 23696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23680 and 23696. First we will calculate the prime factors of 23680 and 23696.

Prime Factorization of 23680

Prime Factorization of 23696

Now multiplying the highest exponent prime factors to calculate the LCM of 23680 and 23696.

LCM(23680,23696) = 2⁷ × 5¹ × 37¹ × 1481¹
LCM(23680,23696) = 35070080