What is the Least Common Multiple of 9 and 27?
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 27 is 27.
LCM(9,27) = 27
Least Common Multiple of 9 and 27 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 27, than apply into the LCM equation.
GCF(9,27) = 9
LCM(9,27) = ( 9 × 27) / 9
LCM(9,27) = 243 / 9
LCM(9,27) = 27
Least Common Multiple (LCM) of 9 and 27 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 27. First we will calculate the prime factors of 9 and 27.
Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:
9 = 32
Prime Factorization of 27
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 27.
LCM(9,27) = 33
LCM(9,27) = 27