What is the Least Common Multiple of 5200 and 5205?

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 5205 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 5205, than apply into the LCM equation.

GCF(5200,5205) = 5
LCM(5200,5205) = ( 5200 × 5205) / 5
LCM(5200,5205) = 27066000 / 5
LCM(5200,5205) = 5413200

Least Common Multiple (LCM) of 5200 and 5205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5200 and 5205. First we will calculate the prime factors of 5200 and 5205.

Prime Factorization of 5200

Prime Factorization of 5205

Now multiplying the highest exponent prime factors to calculate the LCM of 5200 and 5205.

LCM(5200,5205) = 2⁴ × 5² × 13¹ × 3¹ × 347¹
LCM(5200,5205) = 5413200