What is the Least Common Multiple of 17985 and 17994?

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 17994 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 17994, than apply into the LCM equation.

GCF(17985,17994) = 3
LCM(17985,17994) = ( 17985 × 17994) / 3
LCM(17985,17994) = 323622090 / 3
LCM(17985,17994) = 107874030

Least Common Multiple (LCM) of 17985 and 17994 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17985 and 17994. First we will calculate the prime factors of 17985 and 17994.

Prime Factorization of 17985

Prime Factorization of 17994

Now multiplying the highest exponent prime factors to calculate the LCM of 17985 and 17994.

LCM(17985,17994) = 3¹ × 5¹ × 11¹ × 109¹ × 2¹ × 2999¹
LCM(17985,17994) = 107874030