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What is the Least Common Multiple of 3209 and 3213?

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 3209 and 3213 is 10310517.

LCM(3209,3213) = 10310517

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Least Common Multiple of 3209 and 3213 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3209 and 3213, than apply into the LCM equation.

GCF(3209,3213) = 1
LCM(3209,3213) = ( 3209 × 3213) / 1
LCM(3209,3213) = 10310517 / 1
LCM(3209,3213) = 10310517

Least Common Multiple (LCM) of 3209 and 3213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3209 and 3213. First we will calculate the prime factors of 3209 and 3213.

Prime Factorization of 3209

Prime factors of 3209 are 3209. Prime factorization of 3209 in exponential form is:

3209 = 32091

Prime Factorization of 3213

Prime factors of 3213 are 3, 7, 17. Prime factorization of 3213 in exponential form is:

3213 = 33 × 71 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 3209 and 3213.

LCM(3209,3213) = 32091 × 33 × 71 × 171
LCM(3209,3213) = 10310517