What is the Least Common Multiple of 36000 and 36006?

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 36000 and 36006 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36000 and 36006, than apply into the LCM equation.

GCF(36000,36006) = 6
LCM(36000,36006) = ( 36000 × 36006) / 6
LCM(36000,36006) = 1296216000 / 6
LCM(36000,36006) = 216036000

Least Common Multiple (LCM) of 36000 and 36006 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36000 and 36006. First we will calculate the prime factors of 36000 and 36006.

Prime Factorization of 36000

Prime Factorization of 36006

Now multiplying the highest exponent prime factors to calculate the LCM of 36000 and 36006.

LCM(36000,36006) = 2⁵ × 3² × 5³ × 17¹ × 353¹
LCM(36000,36006) = 216036000