What is the Least Common Multiple of 40200 and 40205?

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 40200 and 40205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40200 and 40205, than apply into the LCM equation.

GCF(40200,40205) = 5
LCM(40200,40205) = ( 40200 × 40205) / 5
LCM(40200,40205) = 1616241000 / 5
LCM(40200,40205) = 323248200

Least Common Multiple (LCM) of 40200 and 40205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40200 and 40205. First we will calculate the prime factors of 40200 and 40205.

Prime Factorization of 40200

Prime Factorization of 40205

Now multiplying the highest exponent prime factors to calculate the LCM of 40200 and 40205.

LCM(40200,40205) = 2³ × 3¹ × 5² × 67¹ × 11¹ × 17¹ × 43¹
LCM(40200,40205) = 323248200