What is the Least Common Multiple of 1440 and 1459?

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 1440 and 1459 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1440 and 1459, than apply into the LCM equation.

GCF(1440,1459) = 1
LCM(1440,1459) = ( 1440 × 1459) / 1
LCM(1440,1459) = 2100960 / 1
LCM(1440,1459) = 2100960

Least Common Multiple (LCM) of 1440 and 1459 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1440 and 1459. First we will calculate the prime factors of 1440 and 1459.

Prime Factorization of 1440

Prime Factorization of 1459

Now multiplying the highest exponent prime factors to calculate the LCM of 1440 and 1459.

LCM(1440,1459) = 2⁵ × 3² × 5¹ × 1459¹
LCM(1440,1459) = 2100960