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What is the Least Common Multiple of 1309 and 1321?

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 1309 and 1321 is 1729189.

LCM(1309,1321) = 1729189

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Least Common Multiple of 1309 and 1321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1309 and 1321, than apply into the LCM equation.

GCF(1309,1321) = 1
LCM(1309,1321) = ( 1309 × 1321) / 1
LCM(1309,1321) = 1729189 / 1
LCM(1309,1321) = 1729189

Least Common Multiple (LCM) of 1309 and 1321 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1309 and 1321. First we will calculate the prime factors of 1309 and 1321.

Prime Factorization of 1309

Prime factors of 1309 are 7, 11, 17. Prime factorization of 1309 in exponential form is:

1309 = 71 × 111 × 171

Prime Factorization of 1321

Prime factors of 1321 are 1321. Prime factorization of 1321 in exponential form is:

1321 = 13211

Now multiplying the highest exponent prime factors to calculate the LCM of 1309 and 1321.

LCM(1309,1321) = 71 × 111 × 171 × 13211
LCM(1309,1321) = 1729189