What is the Least Common Multiple of 1404 and 1416?

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 1404 and 1416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1404 and 1416, than apply into the LCM equation.

GCF(1404,1416) = 12
LCM(1404,1416) = ( 1404 × 1416) / 12
LCM(1404,1416) = 1988064 / 12
LCM(1404,1416) = 165672

Least Common Multiple (LCM) of 1404 and 1416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1404 and 1416. First we will calculate the prime factors of 1404 and 1416.

Prime Factorization of 1404

Prime Factorization of 1416

Now multiplying the highest exponent prime factors to calculate the LCM of 1404 and 1416.

LCM(1404,1416) = 2³ × 3³ × 13¹ × 59¹
LCM(1404,1416) = 165672