What is the Least Common Multiple of 11986 and 12000?

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 11986 and 12000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11986 and 12000, than apply into the LCM equation.

GCF(11986,12000) = 2
LCM(11986,12000) = ( 11986 × 12000) / 2
LCM(11986,12000) = 143832000 / 2
LCM(11986,12000) = 71916000

Least Common Multiple (LCM) of 11986 and 12000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 11986 and 12000. First we will calculate the prime factors of 11986 and 12000.

Prime Factorization of 11986

Prime Factorization of 12000

Now multiplying the highest exponent prime factors to calculate the LCM of 11986 and 12000.

LCM(11986,12000) = 2⁵ × 13¹ × 461¹ × 3¹ × 5³
LCM(11986,12000) = 71916000