What is the Least Common Multiple of 9 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 9 and 16 is 144.
LCM(9,16) = 144
Least Common Multiple of 9 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 9 and 16, than apply into the LCM equation.
GCF(9,16) = 1
LCM(9,16) = ( 9 × 16) / 1
LCM(9,16) = 144 / 1
LCM(9,16) = 144
Least Common Multiple (LCM) of 9 and 16 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 16. First we will calculate the prime factors of 9 and 16.
Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:
9 = 32
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 9 and 16.
LCM(9,16) = 32 × 24
LCM(9,16) = 144