What is the Least Common Multiple of 20304 and 20310?

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 20304 and 20310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20304 and 20310, than apply into the LCM equation.

GCF(20304,20310) = 6
LCM(20304,20310) = ( 20304 × 20310) / 6
LCM(20304,20310) = 412374240 / 6
LCM(20304,20310) = 68729040

Least Common Multiple (LCM) of 20304 and 20310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20304 and 20310. First we will calculate the prime factors of 20304 and 20310.

Prime Factorization of 20304

Prime Factorization of 20310

Now multiplying the highest exponent prime factors to calculate the LCM of 20304 and 20310.

LCM(20304,20310) = 2⁴ × 3³ × 47¹ × 5¹ × 677¹
LCM(20304,20310) = 68729040