What is the Least Common Multiple of 1389 and 1407?

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 1389 and 1407 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1389 and 1407, than apply into the LCM equation.

GCF(1389,1407) = 3
LCM(1389,1407) = ( 1389 × 1407) / 3
LCM(1389,1407) = 1954323 / 3
LCM(1389,1407) = 651441

Least Common Multiple (LCM) of 1389 and 1407 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1389 and 1407. First we will calculate the prime factors of 1389 and 1407.

Prime Factorization of 1389

Prime Factorization of 1407

Now multiplying the highest exponent prime factors to calculate the LCM of 1389 and 1407.

LCM(1389,1407) = 3¹ × 463¹ × 7¹ × 67¹
LCM(1389,1407) = 651441