What is the Least Common Multiple of 20509 and 20519?

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 20509 and 20519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20509 and 20519, than apply into the LCM equation.

GCF(20509,20519) = 1
LCM(20509,20519) = ( 20509 × 20519) / 1
LCM(20509,20519) = 420824171 / 1
LCM(20509,20519) = 420824171

Least Common Multiple (LCM) of 20509 and 20519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20509 and 20519. First we will calculate the prime factors of 20509 and 20519.

Prime Factorization of 20509

Prime Factorization of 20519

Now multiplying the highest exponent prime factors to calculate the LCM of 20509 and 20519.

LCM(20509,20519) = 20509¹ × 17² × 71¹
LCM(20509,20519) = 420824171