What is the Least Common Multiple of 2 and 12?
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 2 and 12 is 12.
LCM(2,12) = 12
Least Common Multiple of 2 and 12 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2 and 12, than apply into the LCM equation.
GCF(2,12) = 2
LCM(2,12) = ( 2 × 12) / 2
LCM(2,12) = 24 / 2
LCM(2,12) = 12
Least Common Multiple (LCM) of 2 and 12 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 2 and 12. First we will calculate the prime factors of 2 and 12.
Prime Factorization of 2
Prime factors of 2 are 2. Prime factorization of 2 in exponential form is:
2 = 21
Prime Factorization of 12
Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:
12 = 22 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 2 and 12.
LCM(2,12) = 22 × 31
LCM(2,12) = 12