What is the Least Common Multiple of 1290 and 1296?

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 1290 and 1296 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1290 and 1296, than apply into the LCM equation.

GCF(1290,1296) = 6
LCM(1290,1296) = ( 1290 × 1296) / 6
LCM(1290,1296) = 1671840 / 6
LCM(1290,1296) = 278640

Least Common Multiple (LCM) of 1290 and 1296 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1290 and 1296. First we will calculate the prime factors of 1290 and 1296.

Prime Factorization of 1290

Prime Factorization of 1296

Now multiplying the highest exponent prime factors to calculate the LCM of 1290 and 1296.

LCM(1290,1296) = 2⁴ × 3⁴ × 5¹ × 43¹
LCM(1290,1296) = 278640