What is the Least Common Multiple of 20305 and 20312?

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 20305 and 20312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20305 and 20312, than apply into the LCM equation.

GCF(20305,20312) = 1
LCM(20305,20312) = ( 20305 × 20312) / 1
LCM(20305,20312) = 412435160 / 1
LCM(20305,20312) = 412435160

Least Common Multiple (LCM) of 20305 and 20312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20305 and 20312. First we will calculate the prime factors of 20305 and 20312.

Prime Factorization of 20305

Prime Factorization of 20312

Now multiplying the highest exponent prime factors to calculate the LCM of 20305 and 20312.

LCM(20305,20312) = 5¹ × 31¹ × 131¹ × 2³ × 2539¹
LCM(20305,20312) = 412435160