What is the Least Common Multiple of 1314 and 1320?

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 1314 and 1320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1314 and 1320, than apply into the LCM equation.

GCF(1314,1320) = 6
LCM(1314,1320) = ( 1314 × 1320) / 6
LCM(1314,1320) = 1734480 / 6
LCM(1314,1320) = 289080

Least Common Multiple (LCM) of 1314 and 1320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1314 and 1320. First we will calculate the prime factors of 1314 and 1320.

Prime Factorization of 1314

Prime Factorization of 1320

Now multiplying the highest exponent prime factors to calculate the LCM of 1314 and 1320.

LCM(1314,1320) = 2³ × 3² × 73¹ × 5¹ × 11¹
LCM(1314,1320) = 289080