What is the Least Common Multiple of 7 and 16?
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 16 is 112.
LCM(7,16) = 112
Least Common Multiple of 7 and 16 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 16, than apply into the LCM equation.
GCF(7,16) = 1
LCM(7,16) = ( 7 × 16) / 1
LCM(7,16) = 112 / 1
LCM(7,16) = 112
Least Common Multiple (LCM) of 7 and 16 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 16. First we will calculate the prime factors of 7 and 16.
Prime Factorization of 7
Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:
7 = 71
Prime Factorization of 16
Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:
16 = 24
Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 16.
LCM(7,16) = 71 × 24
LCM(7,16) = 112