What is the Least Common Multiple of 35985 and 36000?

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 35985 and 36000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35985 and 36000, than apply into the LCM equation.

GCF(35985,36000) = 15
LCM(35985,36000) = ( 35985 × 36000) / 15
LCM(35985,36000) = 1295460000 / 15
LCM(35985,36000) = 86364000

Least Common Multiple (LCM) of 35985 and 36000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 35985 and 36000. First we will calculate the prime factors of 35985 and 36000.

Prime Factorization of 35985

Prime Factorization of 36000

Now multiplying the highest exponent prime factors to calculate the LCM of 35985 and 36000.

LCM(35985,36000) = 3² × 5³ × 2399¹ × 2⁵
LCM(35985,36000) = 86364000