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What is the Least Common Multiple of 14 and 34?

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 14 and 34 is 238.

LCM(14,34) = 238

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Least Common Multiple of 14 and 34 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 34, than apply into the LCM equation.

GCF(14,34) = 2
LCM(14,34) = ( 14 × 34) / 2
LCM(14,34) = 476 / 2
LCM(14,34) = 238

Least Common Multiple (LCM) of 14 and 34 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 34. First we will calculate the prime factors of 14 and 34.

Prime Factorization of 14

Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:

14 = 21 × 71

Prime Factorization of 34

Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:

34 = 21 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 34.

LCM(14,34) = 21 × 71 × 171
LCM(14,34) = 238

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