What is the Least Common Multiple of 71680 and 71696?

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 71680 and 71696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71680 and 71696, than apply into the LCM equation.

GCF(71680,71696) = 16
LCM(71680,71696) = ( 71680 × 71696) / 16
LCM(71680,71696) = 5139169280 / 16
LCM(71680,71696) = 321198080

Least Common Multiple (LCM) of 71680 and 71696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71680 and 71696. First we will calculate the prime factors of 71680 and 71696.

Prime Factorization of 71680

Prime Factorization of 71696

Now multiplying the highest exponent prime factors to calculate the LCM of 71680 and 71696.

LCM(71680,71696) = 2¹¹ × 5¹ × 7¹ × 4481¹
LCM(71680,71696) = 321198080