What is the Least Common Multiple of 16 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 16 and 17 is 272.
LCM(16,17) = 272
Least Common Multiple of 16 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 16 and 17, than apply into the LCM equation.
GCF(16,17) = 1
LCM(16,17) = ( 16 × 17) / 1
LCM(16,17) = 272 / 1
LCM(16,17) = 272
Least Common Multiple (LCM) of 16 and 17 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 16 and 17. First we will calculate the prime factors of 16 and 17.
Prime Factorization of 16
Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:
16 = 24
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 16 and 17.
LCM(16,17) = 24 × 171
LCM(16,17) = 272