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What is the Least Common Multiple of 3198 and 3214?

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 3198 and 3214 is 5139186.

LCM(3198,3214) = 5139186

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Least Common Multiple of 3198 and 3214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3198 and 3214, than apply into the LCM equation.

GCF(3198,3214) = 2
LCM(3198,3214) = ( 3198 × 3214) / 2
LCM(3198,3214) = 10278372 / 2
LCM(3198,3214) = 5139186

Least Common Multiple (LCM) of 3198 and 3214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3198 and 3214. First we will calculate the prime factors of 3198 and 3214.

Prime Factorization of 3198

Prime factors of 3198 are 2, 3, 13, 41. Prime factorization of 3198 in exponential form is:

3198 = 21 × 31 × 131 × 411

Prime Factorization of 3214

Prime factors of 3214 are 2, 1607. Prime factorization of 3214 in exponential form is:

3214 = 21 × 16071

Now multiplying the highest exponent prime factors to calculate the LCM of 3198 and 3214.

LCM(3198,3214) = 21 × 31 × 131 × 411 × 16071
LCM(3198,3214) = 5139186