Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 12 and 32 the smallest integer that is 96 that is divisible by both numbers.
Least Common Multiple (LCM) of 12 and 32 is 96.
LCM(12,32) = 96
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 12 and 32. First we will calculate the prime factors of 12 and 32.
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
Prime Factorization of 32
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:
32 = 25
Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 32.
LCM(12,32) = 25×31
LCM(12,32) = 96
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1, 2, 4, 8, 16, 32
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 32, than apply into the LCM equation.
GCF(12,32) = 4
LCM(12,32) = ( 12 × 32) / 4
LCM(12,32) = 384 / 4
LCM(12,32) = 96
(i) The LCM of 32 and 12 is associative
LCM of 12 and 32 = LCM of 32 and 12
1. What is the LCM of 12 and 32?
Answer: LCM of 12 and 32 is 96.
2. 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.
3. What are the Factors of 32?
Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.
4. How to Find the LCM of 12 and 32?
Answer:
Least Common Multiple of 12 and 32 = 96
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 32
32 = 2 x 2 x 2 x 2 x 2
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 96 = 2 x 2 x 2 x 2 x 2 x 3
Step 4: Therefore, the least common multiple of 12 and 32 is 96.