What is the Least Common Multiple of 10320 and 10338?

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 10320 and 10338 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10320 and 10338, than apply into the LCM equation.

GCF(10320,10338) = 6
LCM(10320,10338) = ( 10320 × 10338) / 6
LCM(10320,10338) = 106688160 / 6
LCM(10320,10338) = 17781360

Least Common Multiple (LCM) of 10320 and 10338 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10320 and 10338. First we will calculate the prime factors of 10320 and 10338.

Prime Factorization of 10320

Prime Factorization of 10338

Now multiplying the highest exponent prime factors to calculate the LCM of 10320 and 10338.

LCM(10320,10338) = 2⁴ × 3¹ × 5¹ × 43¹ × 1723¹
LCM(10320,10338) = 17781360