What is the Least Common Multiple of 289 and 296?

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 289 and 296 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 289 and 296, than apply into the LCM equation.

GCF(289,296) = 1
LCM(289,296) = ( 289 × 296) / 1
LCM(289,296) = 85544 / 1
LCM(289,296) = 85544

Least Common Multiple (LCM) of 289 and 296 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 289 and 296. First we will calculate the prime factors of 289 and 296.

Prime Factorization of 289

Prime Factorization of 296

Now multiplying the highest exponent prime factors to calculate the LCM of 289 and 296.

LCM(289,296) = 17² × 2³ × 37¹
LCM(289,296) = 85544