What is the Least Common Multiple of 17680 and 17689?

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 17680 and 17689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17680 and 17689, than apply into the LCM equation.

GCF(17680,17689) = 1
LCM(17680,17689) = ( 17680 × 17689) / 1
LCM(17680,17689) = 312741520 / 1
LCM(17680,17689) = 312741520

Least Common Multiple (LCM) of 17680 and 17689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17680 and 17689. First we will calculate the prime factors of 17680 and 17689.

Prime Factorization of 17680

Prime Factorization of 17689

Now multiplying the highest exponent prime factors to calculate the LCM of 17680 and 17689.

LCM(17680,17689) = 2⁴ × 5¹ × 13¹ × 17¹ × 7² × 19²
LCM(17680,17689) = 312741520