Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 15 and 29 the smallest integer that is 435 that is divisible by both numbers.
Least Common Multiple (LCM) of 15 and 29 is 435.
LCM(15,29) = 435
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 15 and 29. First we will calculate the prime factors of 15 and 29.
Prime Factorization of 15
3 | 15 |
5 | 5 |
1 |
Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:
15 = 31×51
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 15 and 29.
LCM(15,29) = 31×51×291
LCM(15,29) = 435
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1, 3, 5, 15
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 15 and 29, than apply into the LCM equation.
GCF(15,29) = 1
LCM(15,29) = ( 15 × 29) / 1
LCM(15,29) = 435 / 1
LCM(15,29) = 435
(i) The LCM of 29 and 15 is associative
LCM of 15 and 29 = LCM of 29 and 15
1. What is the LCM of 15 and 29?
Answer: LCM of 15 and 29 is 435.
2. What are the Factors of 15?
Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.
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 15 and 29?
Answer:
Least Common Multiple of 15 and 29 = 435
Step 1: Find the prime factorization of 15
15 = 3 x 5
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 = 435 = 3 x 5 x 29
Step 4: Therefore, the least common multiple of 15 and 29 is 435.