What is the Least Common Multiple of 39264 and 39270?

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 39270 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 39270, than apply into the LCM equation.

GCF(39264,39270) = 6
LCM(39264,39270) = ( 39264 × 39270) / 6
LCM(39264,39270) = 1541897280 / 6
LCM(39264,39270) = 256982880

Least Common Multiple (LCM) of 39264 and 39270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39264 and 39270. First we will calculate the prime factors of 39264 and 39270.

Prime Factorization of 39264

Prime Factorization of 39270

Now multiplying the highest exponent prime factors to calculate the LCM of 39264 and 39270.

LCM(39264,39270) = 2⁵ × 3¹ × 409¹ × 5¹ × 7¹ × 11¹ × 17¹
LCM(39264,39270) = 256982880