What is the Least Common Multiple of 34314 and 34320?

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 34314 and 34320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34314 and 34320, than apply into the LCM equation.

GCF(34314,34320) = 6
LCM(34314,34320) = ( 34314 × 34320) / 6
LCM(34314,34320) = 1177656480 / 6
LCM(34314,34320) = 196276080

Least Common Multiple (LCM) of 34314 and 34320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34314 and 34320. First we will calculate the prime factors of 34314 and 34320.

Prime Factorization of 34314

Prime Factorization of 34320

Now multiplying the highest exponent prime factors to calculate the LCM of 34314 and 34320.

LCM(34314,34320) = 2⁴ × 3¹ × 7¹ × 19¹ × 43¹ × 5¹ × 11¹ × 13¹
LCM(34314,34320) = 196276080