What is the Least Common Multiple of 3 and 18?
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 3 and 18 is 18.
LCM(3,18) = 18
Least Common Multiple of 3 and 18 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 18, than apply into the LCM equation.
GCF(3,18) = 3
LCM(3,18) = ( 3 × 18) / 3
LCM(3,18) = 54 / 3
LCM(3,18) = 18
Least Common Multiple (LCM) of 3 and 18 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 18. First we will calculate the prime factors of 3 and 18.
Prime Factorization of 3
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
Prime Factorization of 18
Prime factors of 18 are 2, 3. Prime factorization of 18 in exponential form is:
18 = 21 × 32
Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 18.
LCM(3,18) = 32 × 21
LCM(3,18) = 18