What is the Least Common Multiple of 3 and 16?
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 16 is 48.
LCM(3,16) = 48
Least Common Multiple of 3 and 16 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 16, than apply into the LCM equation.
GCF(3,16) = 1
LCM(3,16) = ( 3 × 16) / 1
LCM(3,16) = 48 / 1
LCM(3,16) = 48
Least Common Multiple (LCM) of 3 and 16 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 16. First we will calculate the prime factors of 3 and 16.
Prime Factorization of 3
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
Prime Factorization of 16
Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:
16 = 24
Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 16.
LCM(3,16) = 31 × 24
LCM(3,16) = 48