What is the Least Common Multiple of 1400 and 1404?

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 1400 and 1404 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1400 and 1404, than apply into the LCM equation.

GCF(1400,1404) = 4
LCM(1400,1404) = ( 1400 × 1404) / 4
LCM(1400,1404) = 1965600 / 4
LCM(1400,1404) = 491400

Least Common Multiple (LCM) of 1400 and 1404 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1400 and 1404. First we will calculate the prime factors of 1400 and 1404.

Prime Factorization of 1400

Prime Factorization of 1404

Now multiplying the highest exponent prime factors to calculate the LCM of 1400 and 1404.

LCM(1400,1404) = 2³ × 5² × 7¹ × 3³ × 13¹
LCM(1400,1404) = 491400