What is the Least Common Multiple of 78138 and 78144?

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 78138 and 78144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78138 and 78144, than apply into the LCM equation.

GCF(78138,78144) = 6
LCM(78138,78144) = ( 78138 × 78144) / 6
LCM(78138,78144) = 6106015872 / 6
LCM(78138,78144) = 1017669312

Least Common Multiple (LCM) of 78138 and 78144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78138 and 78144. First we will calculate the prime factors of 78138 and 78144.

Prime Factorization of 78138

Prime Factorization of 78144

Now multiplying the highest exponent prime factors to calculate the LCM of 78138 and 78144.

LCM(78138,78144) = 2⁶ × 3³ × 1447¹ × 11¹ × 37¹
LCM(78138,78144) = 1017669312