What is the Least Common Multiple of 20208 and 20219?

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 20208 and 20219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20208 and 20219, than apply into the LCM equation.

GCF(20208,20219) = 1
LCM(20208,20219) = ( 20208 × 20219) / 1
LCM(20208,20219) = 408585552 / 1
LCM(20208,20219) = 408585552

Least Common Multiple (LCM) of 20208 and 20219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20208 and 20219. First we will calculate the prime factors of 20208 and 20219.

Prime Factorization of 20208

Prime Factorization of 20219

Now multiplying the highest exponent prime factors to calculate the LCM of 20208 and 20219.

LCM(20208,20219) = 2⁴ × 3¹ × 421¹ × 20219¹
LCM(20208,20219) = 408585552