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Least Common Multiple of 6 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 6 and 34 is 102.

LCM(6,34) = 102

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Least Common Multiple of 6 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 6 and 34, than apply into the LCM equation.

GCF(6,34) = 2
LCM(6,34) = ( 6 × 34) / 2
LCM(6,34) = 204 / 2
LCM(6,34) = 102

Least Common Multiple (LCM) of 6 and 34 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 34. First we will calculate the prime factors of 6 and 34.

Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 21 × 31

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 6 and 34.

LCM(6,34) = 21 × 31 × 171
LCM(6,34) = 102

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