What is the Least Common Multiple of 17985 and 17996?

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 17985 and 17996 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17985 and 17996, than apply into the LCM equation.

GCF(17985,17996) = 11
LCM(17985,17996) = ( 17985 × 17996) / 11
LCM(17985,17996) = 323658060 / 11
LCM(17985,17996) = 29423460

Least Common Multiple (LCM) of 17985 and 17996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17985 and 17996. First we will calculate the prime factors of 17985 and 17996.

Prime Factorization of 17985

Prime Factorization of 17996

Now multiplying the highest exponent prime factors to calculate the LCM of 17985 and 17996.

LCM(17985,17996) = 3¹ × 5¹ × 11¹ × 109¹ × 2² × 409¹
LCM(17985,17996) = 29423460