What is the Least Common Multiple of 7 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 7 and 17 is 119.
LCM(7,17) = 119
Least Common Multiple of 7 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 7 and 17, than apply into the LCM equation.
GCF(7,17) = 1
LCM(7,17) = ( 7 × 17) / 1
LCM(7,17) = 119 / 1
LCM(7,17) = 119
Least Common Multiple (LCM) of 7 and 17 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 17. First we will calculate the prime factors of 7 and 17.
Prime Factorization of 7
Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:
7 = 71
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 7 and 17.
LCM(7,17) = 71 × 171
LCM(7,17) = 119