What is the Least Common Multiple of 1260 and 1280?

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 1260 and 1280 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1260 and 1280, than apply into the LCM equation.

GCF(1260,1280) = 20
LCM(1260,1280) = ( 1260 × 1280) / 20
LCM(1260,1280) = 1612800 / 20
LCM(1260,1280) = 80640

Least Common Multiple (LCM) of 1260 and 1280 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1260 and 1280. First we will calculate the prime factors of 1260 and 1280.

Prime Factorization of 1260

Prime Factorization of 1280

Now multiplying the highest exponent prime factors to calculate the LCM of 1260 and 1280.

LCM(1260,1280) = 2⁸ × 3² × 5¹ × 7¹
LCM(1260,1280) = 80640