What is the Least Common Multiple of 9 and 33?
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 33 is 99.
LCM(9,33) = 99
Least Common Multiple of 9 and 33 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 33, than apply into the LCM equation.
GCF(9,33) = 3
LCM(9,33) = ( 9 × 33) / 3
LCM(9,33) = 297 / 3
LCM(9,33) = 99
Least Common Multiple (LCM) of 9 and 33 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 33. First we will calculate the prime factors of 9 and 33.
Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:
9 = 32
Prime Factorization of 33
Prime factors of 33 are 3, 11. Prime factorization of 33 in exponential form is:
33 = 31 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 33.
LCM(9,33) = 32 × 111
LCM(9,33) = 99