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What is the Least Common Multiple of 1304 and 1314?

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 (LCM) of 1304 and 1314 is 856728.

LCM(1304,1314) = 856728

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Least Common Multiple of 1304 and 1314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1304 and 1314, than apply into the LCM equation.

GCF(1304,1314) = 2
LCM(1304,1314) = ( 1304 × 1314) / 2
LCM(1304,1314) = 1713456 / 2
LCM(1304,1314) = 856728

Least Common Multiple (LCM) of 1304 and 1314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1304 and 1314. First we will calculate the prime factors of 1304 and 1314.

Prime Factorization of 1304

Prime factors of 1304 are 2, 163. Prime factorization of 1304 in exponential form is:

1304 = 23 × 1631

Prime Factorization of 1314

Prime factors of 1314 are 2, 3, 73. Prime factorization of 1314 in exponential form is:

1314 = 21 × 32 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 1304 and 1314.

LCM(1304,1314) = 23 × 1631 × 32 × 731
LCM(1304,1314) = 856728