What is the Least Common Multiple of 12 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 12 and 16 is 48.
LCM(12,16) = 48
Least Common Multiple of 12 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 12 and 16, than apply into the LCM equation.
GCF(12,16) = 4
LCM(12,16) = ( 12 × 16) / 4
LCM(12,16) = 192 / 4
LCM(12,16) = 48
Least Common Multiple (LCM) of 12 and 16 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 16. First we will calculate the prime factors of 12 and 16.
Prime Factorization of 12
Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:
12 = 22 × 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 12 and 16.
LCM(12,16) = 24 × 31
LCM(12,16) = 48