Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2 and 12 the smallest integer that is 12 that is divisible by both numbers.
Least Common Multiple (LCM) of 2 and 12 is 12.
LCM(2,12) = 12
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
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
2 | 2 |
1 |
Prime factors of 2 are 2. Prime factorization of 2 in exponential form is:
2 = 21
Prime Factorization of 12
2 | 12 |
2 | 6 |
3 | 3 |
1 |
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
Factors of 2
List of positive integer factors of 2 that divides 2 without a remainder.
1, 2
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
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
(i) The LCM of 12 and 2 is associative
LCM of 2 and 12 = LCM of 12 and 2
1. What is the LCM of 2 and 12?
Answer: LCM of 2 and 12 is 12.
2. What are the Factors of 2?
Answer: Factors of 2 are 1, 2. There are 2 integers that are factors of 2. The greatest factor of 2 is 2.
3. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
4. How to Find the LCM of 2 and 12?
Answer:
Least Common Multiple of 2 and 12 = 12
Step 1: Find the prime factorization of 2
2 = 2
Step 2: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12 = 2 x 2 x 3
Step 4: Therefore, the least common multiple of 2 and 12 is 12.