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