What is the Least Common Multiple of 10689 and 10704?

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 10689 and 10704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10689 and 10704, than apply into the LCM equation.

GCF(10689,10704) = 3
LCM(10689,10704) = ( 10689 × 10704) / 3
LCM(10689,10704) = 114415056 / 3
LCM(10689,10704) = 38138352

Least Common Multiple (LCM) of 10689 and 10704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10689 and 10704. First we will calculate the prime factors of 10689 and 10704.

Prime Factorization of 10689

Prime Factorization of 10704

Now multiplying the highest exponent prime factors to calculate the LCM of 10689 and 10704.

LCM(10689,10704) = 3¹ × 7¹ × 509¹ × 2⁴ × 223¹
LCM(10689,10704) = 38138352