What is the Least Common Multiple of 1420 and 1440?

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 1420 and 1440 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1420 and 1440, than apply into the LCM equation.

GCF(1420,1440) = 20
LCM(1420,1440) = ( 1420 × 1440) / 20
LCM(1420,1440) = 2044800 / 20
LCM(1420,1440) = 102240

Least Common Multiple (LCM) of 1420 and 1440 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1420 and 1440. First we will calculate the prime factors of 1420 and 1440.

Prime Factorization of 1420

Prime Factorization of 1440

Now multiplying the highest exponent prime factors to calculate the LCM of 1420 and 1440.

LCM(1420,1440) = 2⁵ × 5¹ × 71¹ × 3²
LCM(1420,1440) = 102240