What is the Least Common Multiple of 16314 and 16320?

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 16314 and 16320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16314 and 16320, than apply into the LCM equation.

GCF(16314,16320) = 6
LCM(16314,16320) = ( 16314 × 16320) / 6
LCM(16314,16320) = 266244480 / 6
LCM(16314,16320) = 44374080

Least Common Multiple (LCM) of 16314 and 16320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16314 and 16320. First we will calculate the prime factors of 16314 and 16320.

Prime Factorization of 16314

Prime Factorization of 16320

Now multiplying the highest exponent prime factors to calculate the LCM of 16314 and 16320.

LCM(16314,16320) = 2⁶ × 3¹ × 2719¹ × 5¹ × 17¹
LCM(16314,16320) = 44374080