What is the Least Common Multiple of 17970 and 17980?

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 17970 and 17980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17970 and 17980, than apply into the LCM equation.

GCF(17970,17980) = 10
LCM(17970,17980) = ( 17970 × 17980) / 10
LCM(17970,17980) = 323100600 / 10
LCM(17970,17980) = 32310060

Least Common Multiple (LCM) of 17970 and 17980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17970 and 17980. First we will calculate the prime factors of 17970 and 17980.

Prime Factorization of 17970

Prime Factorization of 17980

Now multiplying the highest exponent prime factors to calculate the LCM of 17970 and 17980.

LCM(17970,17980) = 2² × 3¹ × 5¹ × 599¹ × 29¹ × 31¹
LCM(17970,17980) = 32310060