What is the Least Common Multiple of 9 and 8?
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 8 is 72.
LCM(9,8) = 72
Least Common Multiple of 9 and 8 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 8, than apply into the LCM equation.
GCF(9,8) = 1
LCM(9,8) = ( 9 × 8) / 1
LCM(9,8) = 72 / 1
LCM(9,8) = 72
Least Common Multiple (LCM) of 9 and 8 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 8. First we will calculate the prime factors of 9 and 8.
Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:
9 = 32
Prime Factorization of 8
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:
8 = 23
Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 8.
LCM(9,8) = 32 × 23
LCM(9,8) = 72