What is the Least Common Multiple of 20208 and 20216?

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 20216 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 20216, than apply into the LCM equation.

GCF(20208,20216) = 8
LCM(20208,20216) = ( 20208 × 20216) / 8
LCM(20208,20216) = 408524928 / 8
LCM(20208,20216) = 51065616

Least Common Multiple (LCM) of 20208 and 20216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20208 and 20216. First we will calculate the prime factors of 20208 and 20216.

Prime Factorization of 20208

Prime Factorization of 20216

Now multiplying the highest exponent prime factors to calculate the LCM of 20208 and 20216.

LCM(20208,20216) = 2⁴ × 3¹ × 421¹ × 7¹ × 19²
LCM(20208,20216) = 51065616