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 29 the smallest integer that is 348 that is divisible by both numbers.
Least Common Multiple (LCM) of 12 and 29 is 348.
LCM(12,29) = 348
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 29. First we will calculate the prime factors of 12 and 29.
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 29
29 | 29 |
1 |
Prime factors of 29 are 29. Prime factorization of 29 in exponential form is:
29 = 291
Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 29.
LCM(12,29) = 22×31×291
LCM(12,29) = 348
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Factors of 29
List of positive integer factors of 29 that divides 29 without a remainder.
1, 29
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 29, than apply into the LCM equation.
GCF(12,29) = 1
LCM(12,29) = ( 12 × 29) / 1
LCM(12,29) = 348 / 1
LCM(12,29) = 348
(i) The LCM of 29 and 12 is associative
LCM of 12 and 29 = LCM of 29 and 12
1. What is the LCM of 12 and 29?
Answer: LCM of 12 and 29 is 348.
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 29?
Answer: Factors of 29 are 1, 29. There are 2 integers that are factors of 29. The greatest factor of 29 is 29.
4. How to Find the LCM of 12 and 29?
Answer:
Least Common Multiple of 12 and 29 = 348
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 29
29 = 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 348 = 2 x 2 x 3 x 29
Step 4: Therefore, the least common multiple of 12 and 29 is 348.