What is the Least Common Multiple of 15 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 15 and 33 is 165.
LCM(15,33) = 165
Least Common Multiple of 15 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 15 and 33, than apply into the LCM equation.
GCF(15,33) = 3
LCM(15,33) = ( 15 × 33) / 3
LCM(15,33) = 495 / 3
LCM(15,33) = 165
Least Common Multiple (LCM) of 15 and 33 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 33. First we will calculate the prime factors of 15 and 33.
Prime Factorization of 15
Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:
15 = 31 × 51
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 15 and 33.
LCM(15,33) = 31 × 51 × 111
LCM(15,33) = 165