What is the Least Common Multiple of 289 and 300?

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 300 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 300, than apply into the LCM equation.

GCF(289,300) = 1
LCM(289,300) = ( 289 × 300) / 1
LCM(289,300) = 86700 / 1
LCM(289,300) = 86700

Least Common Multiple (LCM) of 289 and 300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 289 and 300. First we will calculate the prime factors of 289 and 300.

Prime Factorization of 289

Prime Factorization of 300

Now multiplying the highest exponent prime factors to calculate the LCM of 289 and 300.

LCM(289,300) = 17² × 2² × 3¹ × 5²
LCM(289,300) = 86700