What is the Least Common Multiple of 8200 and 8205?

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 8200 and 8205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8200 and 8205, than apply into the LCM equation.

GCF(8200,8205) = 5
LCM(8200,8205) = ( 8200 × 8205) / 5
LCM(8200,8205) = 67281000 / 5
LCM(8200,8205) = 13456200

Least Common Multiple (LCM) of 8200 and 8205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8200 and 8205. First we will calculate the prime factors of 8200 and 8205.

Prime Factorization of 8200

Prime Factorization of 8205

Now multiplying the highest exponent prime factors to calculate the LCM of 8200 and 8205.

LCM(8200,8205) = 2³ × 5² × 41¹ × 3¹ × 547¹
LCM(8200,8205) = 13456200