What is the Least Common Multiple of 270 and 289?

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 270 and 289 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 270 and 289, than apply into the LCM equation.

GCF(270,289) = 1
LCM(270,289) = ( 270 × 289) / 1
LCM(270,289) = 78030 / 1
LCM(270,289) = 78030

Least Common Multiple (LCM) of 270 and 289 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 270 and 289. First we will calculate the prime factors of 270 and 289.

Prime Factorization of 270

Prime Factorization of 289

Now multiplying the highest exponent prime factors to calculate the LCM of 270 and 289.

LCM(270,289) = 2¹ × 3³ × 5¹ × 17²
LCM(270,289) = 78030