What is the Least Common Multiple of 5200 and 5209?

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 5200 and 5209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5200 and 5209, than apply into the LCM equation.

GCF(5200,5209) = 1
LCM(5200,5209) = ( 5200 × 5209) / 1
LCM(5200,5209) = 27086800 / 1
LCM(5200,5209) = 27086800

Least Common Multiple (LCM) of 5200 and 5209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5200 and 5209. First we will calculate the prime factors of 5200 and 5209.

Prime Factorization of 5200

Prime Factorization of 5209

Now multiplying the highest exponent prime factors to calculate the LCM of 5200 and 5209.

LCM(5200,5209) = 2⁴ × 5² × 13¹ × 5209¹
LCM(5200,5209) = 27086800