What is the Least Common Multiple of 6 and 17?
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 17 is 102.
LCM(6,17) = 102
Least Common Multiple of 6 and 17 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 17, than apply into the LCM equation.
GCF(6,17) = 1
LCM(6,17) = ( 6 × 17) / 1
LCM(6,17) = 102 / 1
LCM(6,17) = 102
Least Common Multiple (LCM) of 6 and 17 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 17. First we will calculate the prime factors of 6 and 17.
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 17
Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:
17 = 171
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 17.
LCM(6,17) = 21 × 31 × 171
LCM(6,17) = 102