What is the Least Common Multiple of 9 and 15?
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 15 is 45.
LCM(9,15) = 45
Least Common Multiple of 9 and 15 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 15, than apply into the LCM equation.
GCF(9,15) = 3
LCM(9,15) = ( 9 × 15) / 3
LCM(9,15) = 135 / 3
LCM(9,15) = 45
Least Common Multiple (LCM) of 9 and 15 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 15. First we will calculate the prime factors of 9 and 15.
Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:
9 = 32
Prime Factorization of 15
Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:
15 = 31 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 15.
LCM(9,15) = 32 × 51
LCM(9,15) = 45