What is the Least Common Multiple of 39264 and 39284?

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 39264 and 39284 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39264 and 39284, than apply into the LCM equation.

GCF(39264,39284) = 4
LCM(39264,39284) = ( 39264 × 39284) / 4
LCM(39264,39284) = 1542446976 / 4
LCM(39264,39284) = 385611744

Least Common Multiple (LCM) of 39264 and 39284 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39264 and 39284. First we will calculate the prime factors of 39264 and 39284.

Prime Factorization of 39264

Prime Factorization of 39284

Now multiplying the highest exponent prime factors to calculate the LCM of 39264 and 39284.

LCM(39264,39284) = 2⁵ × 3¹ × 409¹ × 7¹ × 23¹ × 61¹
LCM(39264,39284) = 385611744