What is the Least Common Multiple of 13974 and 13989?

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 13974 and 13989 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13974 and 13989, than apply into the LCM equation.

GCF(13974,13989) = 3
LCM(13974,13989) = ( 13974 × 13989) / 3
LCM(13974,13989) = 195482286 / 3
LCM(13974,13989) = 65160762

Least Common Multiple (LCM) of 13974 and 13989 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13974 and 13989. First we will calculate the prime factors of 13974 and 13989.

Prime Factorization of 13974

Prime Factorization of 13989

Now multiplying the highest exponent prime factors to calculate the LCM of 13974 and 13989.

LCM(13974,13989) = 2¹ × 3¹ × 17¹ × 137¹ × 4663¹
LCM(13974,13989) = 65160762