What is the Least Common Multiple of 1989 and 2006?

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 1989 and 2006 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1989 and 2006, than apply into the LCM equation.

GCF(1989,2006) = 17
LCM(1989,2006) = ( 1989 × 2006) / 17
LCM(1989,2006) = 3989934 / 17
LCM(1989,2006) = 234702

Least Common Multiple (LCM) of 1989 and 2006 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1989 and 2006. First we will calculate the prime factors of 1989 and 2006.

Prime Factorization of 1989

Prime Factorization of 2006

Now multiplying the highest exponent prime factors to calculate the LCM of 1989 and 2006.

LCM(1989,2006) = 3² × 13¹ × 17¹ × 2¹ × 59¹
LCM(1989,2006) = 234702