What is the Least Common Multiple of 17980 and 18000?

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 17980 and 18000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17980 and 18000, than apply into the LCM equation.

GCF(17980,18000) = 20
LCM(17980,18000) = ( 17980 × 18000) / 20
LCM(17980,18000) = 323640000 / 20
LCM(17980,18000) = 16182000

Least Common Multiple (LCM) of 17980 and 18000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17980 and 18000. First we will calculate the prime factors of 17980 and 18000.

Prime Factorization of 17980

Prime Factorization of 18000

Now multiplying the highest exponent prime factors to calculate the LCM of 17980 and 18000.

LCM(17980,18000) = 2⁴ × 5³ × 29¹ × 31¹ × 3²
LCM(17980,18000) = 16182000