Least Common Multiple of 414 and 415
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 414 and 415 the smallest integer that is 171810 that is divisible by both numbers.
Least Common Multiple (LCM) of 414 and 415 is 171810.
LCM(414,415) = 171810
LCM of 414 and 415
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 414 and 415 by Prime method
- Least Common Multiple of 414 and 415 with GCF Formula
LCM of 414 and 415 is 171810
Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 415. First we will calculate the prime factors of 414 and 415.
Prime Factorization of 414
| 2 | 414 |
| 3 | 207 |
| 3 | 69 |
| 23 | 23 |
| 1 |
Prime factors of 414 are 2, 3,23. Prime factorization of 414 in exponential form is:
414 = 21×32×231
Prime Factorization of 415
| 5 | 415 |
| 83 | 83 |
| 1 |
Prime factors of 415 are 5,83. Prime factorization of 415 in exponential form is:
415 = 51×831
Now multiplying the highest exponent prime factors to calculate the LCM of 414 and 415.
LCM(414,415) = 21×32×51×231×831
LCM(414,415) = 171810
Factors of 414
List of positive integer factors of 414 that divides 414 without a remainder.
1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
Factors of 415
List of positive integer factors of 415 that divides 415 without a remainder.
1, 5, 83, 415
Least Common Multiple of 414 and 415 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 414 and 415, than apply into the LCM equation.
GCF(414,415) = 1
LCM(414,415) = ( 414 × 415) / 1
LCM(414,415) = 171810 / 1
LCM(414,415) = 171810
Properties of LCM 414 and 415
(i) The LCM of 415 and 414 is associative
LCM of 414 and 415 = LCM of 415 and 414
Related Least Common Multiples of 414
Related Least Common Multiples of 415
Frequently Asked Questions on LCM of 414 and 415
1. What is the LCM of 414 and 415?
Answer: LCM of 414 and 415 is 171810.
2. What are the Factors of 414?
Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.
3. What are the Factors of 415?
Answer: Factors of 415 are 1, 5, 83, 415. There are 4 integers that are factors of 415. The greatest factor of 415 is 415.
4. How to Find the LCM of 414 and 415?
Answer:
Least Common Multiple of 414 and 415 = 171810
Step 1: Find the prime factorization of 414
414 = 2 x 3 x 3 x 23
Step 2: Find the prime factorization of 415
415 = 5 x 83
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 171810 = 2 x 3 x 3 x 5 x 23 x 83
Step 4: Therefore, the least common multiple of 414 and 415 is 171810.