What is the Least Common Multiple of 67305 and 67314?

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 67305 and 67314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67305 and 67314, than apply into the LCM equation.

GCF(67305,67314) = 3
LCM(67305,67314) = ( 67305 × 67314) / 3
LCM(67305,67314) = 4530568770 / 3
LCM(67305,67314) = 1510189590

Least Common Multiple (LCM) of 67305 and 67314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67305 and 67314. First we will calculate the prime factors of 67305 and 67314.

Prime Factorization of 67305

Prime Factorization of 67314

Now multiplying the highest exponent prime factors to calculate the LCM of 67305 and 67314.

LCM(67305,67314) = 3¹ × 5¹ × 7¹ × 641¹ × 2¹ × 13¹ × 863¹
LCM(67305,67314) = 1510189590