What is the Least Common Multiple of 1407 and 1413?

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 1407 and 1413 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1407 and 1413, than apply into the LCM equation.

GCF(1407,1413) = 3
LCM(1407,1413) = ( 1407 × 1413) / 3
LCM(1407,1413) = 1988091 / 3
LCM(1407,1413) = 662697

Least Common Multiple (LCM) of 1407 and 1413 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1407 and 1413. First we will calculate the prime factors of 1407 and 1413.

Prime Factorization of 1407

Prime Factorization of 1413

Now multiplying the highest exponent prime factors to calculate the LCM of 1407 and 1413.

LCM(1407,1413) = 3² × 7¹ × 67¹ × 157¹
LCM(1407,1413) = 662697