What is the Least Common Multiple of 6 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 6 and 9 is 18.
LCM(6,9) = 18
Least Common Multiple of 6 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 6 and 9, than apply into the LCM equation.
GCF(6,9) = 3
LCM(6,9) = ( 6 × 9) / 3
LCM(6,9) = 54 / 3
LCM(6,9) = 18
Least Common Multiple (LCM) of 6 and 9 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 9. First we will calculate the prime factors of 6 and 9.
Prime Factorization of 6
Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:
6 = 21 × 31
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 6 and 9.
LCM(6,9) = 21 × 32
LCM(6,9) = 18