What is the Least Common Multiple of 71680 and 71688?

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 71688 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 71688, than apply into the LCM equation.

GCF(71680,71688) = 8
LCM(71680,71688) = ( 71680 × 71688) / 8
LCM(71680,71688) = 5138595840 / 8
LCM(71680,71688) = 642324480

Least Common Multiple (LCM) of 71680 and 71688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71680 and 71688. First we will calculate the prime factors of 71680 and 71688.

Prime Factorization of 71680

Prime Factorization of 71688

Now multiplying the highest exponent prime factors to calculate the LCM of 71680 and 71688.

LCM(71680,71688) = 2¹¹ × 5¹ × 7¹ × 3¹ × 29¹ × 103¹
LCM(71680,71688) = 642324480