What is the Least Common Multiple of 390 and 403?

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 390 and 403 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 390 and 403, than apply into the LCM equation.

GCF(390,403) = 13
LCM(390,403) = ( 390 × 403) / 13
LCM(390,403) = 157170 / 13
LCM(390,403) = 12090

Least Common Multiple (LCM) of 390 and 403 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 390 and 403. First we will calculate the prime factors of 390 and 403.

Prime Factorization of 390

Prime Factorization of 403

Now multiplying the highest exponent prime factors to calculate the LCM of 390 and 403.

LCM(390,403) = 2¹ × 3¹ × 5¹ × 13¹ × 31¹
LCM(390,403) = 12090