Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 14 and 29 the smallest integer that is 406 that is divisible by both numbers.
Least Common Multiple (LCM) of 14 and 29 is 406.
LCM(14,29) = 406
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 14 and 29. First we will calculate the prime factors of 14 and 29.
Prime Factorization of 14
2 | 14 |
7 | 7 |
1 |
Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:
14 = 21×71
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 14 and 29.
LCM(14,29) = 21×71×291
LCM(14,29) = 406
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1, 2, 7, 14
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 14 and 29, than apply into the LCM equation.
GCF(14,29) = 1
LCM(14,29) = ( 14 × 29) / 1
LCM(14,29) = 406 / 1
LCM(14,29) = 406
(i) The LCM of 29 and 14 is associative
LCM of 14 and 29 = LCM of 29 and 14
1. What is the LCM of 14 and 29?
Answer: LCM of 14 and 29 is 406.
2. What are the Factors of 14?
Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.
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 14 and 29?
Answer:
Least Common Multiple of 14 and 29 = 406
Step 1: Find the prime factorization of 14
14 = 2 x 7
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 = 406 = 2 x 7 x 29
Step 4: Therefore, the least common multiple of 14 and 29 is 406.