What is the Least Common Multiple of 67296 and 67305?

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 67296 and 67305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67296 and 67305, than apply into the LCM equation.

GCF(67296,67305) = 3
LCM(67296,67305) = ( 67296 × 67305) / 3
LCM(67296,67305) = 4529357280 / 3
LCM(67296,67305) = 1509785760

Least Common Multiple (LCM) of 67296 and 67305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67296 and 67305. First we will calculate the prime factors of 67296 and 67305.

Prime Factorization of 67296

Prime Factorization of 67305

Now multiplying the highest exponent prime factors to calculate the LCM of 67296 and 67305.

LCM(67296,67305) = 2⁵ × 3¹ × 701¹ × 5¹ × 7¹ × 641¹
LCM(67296,67305) = 1509785760