What is the Least Common Multiple of 3200 and 3205?

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 3200 and 3205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3200 and 3205, than apply into the LCM equation.

GCF(3200,3205) = 5
LCM(3200,3205) = ( 3200 × 3205) / 5
LCM(3200,3205) = 10256000 / 5
LCM(3200,3205) = 2051200

Least Common Multiple (LCM) of 3200 and 3205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3200 and 3205. First we will calculate the prime factors of 3200 and 3205.

Prime Factorization of 3200

Prime Factorization of 3205

Now multiplying the highest exponent prime factors to calculate the LCM of 3200 and 3205.

LCM(3200,3205) = 2⁷ × 5² × 641¹
LCM(3200,3205) = 2051200