What is the Least Common Multiple of 5209 and 5213?

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 5209 and 5213 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5209 and 5213, than apply into the LCM equation.

GCF(5209,5213) = 1
LCM(5209,5213) = ( 5209 × 5213) / 1
LCM(5209,5213) = 27154517 / 1
LCM(5209,5213) = 27154517

Least Common Multiple (LCM) of 5209 and 5213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5209 and 5213. First we will calculate the prime factors of 5209 and 5213.

Prime Factorization of 5209

Prime Factorization of 5213

Now multiplying the highest exponent prime factors to calculate the LCM of 5209 and 5213.

LCM(5209,5213) = 5209¹ × 13¹ × 401¹
LCM(5209,5213) = 27154517