What is the Least Common Multiple of 20304 and 20314?

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 20314 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 20314, than apply into the LCM equation.

GCF(20304,20314) = 2
LCM(20304,20314) = ( 20304 × 20314) / 2
LCM(20304,20314) = 412455456 / 2
LCM(20304,20314) = 206227728

Least Common Multiple (LCM) of 20304 and 20314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20304 and 20314. First we will calculate the prime factors of 20304 and 20314.

Prime Factorization of 20304

Prime Factorization of 20314

Now multiplying the highest exponent prime factors to calculate the LCM of 20304 and 20314.

LCM(20304,20314) = 2⁴ × 3³ × 47¹ × 7¹ × 1451¹
LCM(20304,20314) = 206227728