What is the Least Common Multiple of 39072 and 39078?

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 39072 and 39078 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39072 and 39078, than apply into the LCM equation.

GCF(39072,39078) = 6
LCM(39072,39078) = ( 39072 × 39078) / 6
LCM(39072,39078) = 1526855616 / 6
LCM(39072,39078) = 254475936

Least Common Multiple (LCM) of 39072 and 39078 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39072 and 39078. First we will calculate the prime factors of 39072 and 39078.

Prime Factorization of 39072

Prime Factorization of 39078

Now multiplying the highest exponent prime factors to calculate the LCM of 39072 and 39078.

LCM(39072,39078) = 2⁵ × 3² × 11¹ × 37¹ × 13¹ × 167¹
LCM(39072,39078) = 254475936