What is the Least Common Multiple of 13989 and 14004?

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 13989 and 14004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13989 and 14004, than apply into the LCM equation.

GCF(13989,14004) = 3
LCM(13989,14004) = ( 13989 × 14004) / 3
LCM(13989,14004) = 195901956 / 3
LCM(13989,14004) = 65300652

Least Common Multiple (LCM) of 13989 and 14004 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13989 and 14004. First we will calculate the prime factors of 13989 and 14004.

Prime Factorization of 13989

Prime Factorization of 14004

Now multiplying the highest exponent prime factors to calculate the LCM of 13989 and 14004.

LCM(13989,14004) = 3² × 4663¹ × 2² × 389¹
LCM(13989,14004) = 65300652