What is the Least Common Multiple of 1407 and 1415?

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 1415 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 1415, than apply into the LCM equation.

GCF(1407,1415) = 1
LCM(1407,1415) = ( 1407 × 1415) / 1
LCM(1407,1415) = 1990905 / 1
LCM(1407,1415) = 1990905

Least Common Multiple (LCM) of 1407 and 1415 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1407 and 1415. First we will calculate the prime factors of 1407 and 1415.

Prime Factorization of 1407

Prime Factorization of 1415

Now multiplying the highest exponent prime factors to calculate the LCM of 1407 and 1415.

LCM(1407,1415) = 3¹ × 7¹ × 67¹ × 5¹ × 283¹
LCM(1407,1415) = 1990905