What is the Least Common Multiple of 39405 and 39420?

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 39405 and 39420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39405 and 39420, than apply into the LCM equation.

GCF(39405,39420) = 15
LCM(39405,39420) = ( 39405 × 39420) / 15
LCM(39405,39420) = 1553345100 / 15
LCM(39405,39420) = 103556340

Least Common Multiple (LCM) of 39405 and 39420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39405 and 39420. First we will calculate the prime factors of 39405 and 39420.

Prime Factorization of 39405

Prime Factorization of 39420

Now multiplying the highest exponent prime factors to calculate the LCM of 39405 and 39420.

LCM(39405,39420) = 3³ × 5¹ × 37¹ × 71¹ × 2² × 73¹
LCM(39405,39420) = 103556340