Least Common Multiple of 413 and 414
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 413 and 414 the smallest integer that is 170982 that is divisible by both numbers.
Least Common Multiple (LCM) of 413 and 414 is 170982.
LCM(413,414) = 170982
LCM of 413 and 414
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 413 and 414 by Prime method
- Least Common Multiple of 413 and 414 with GCF Formula
LCM of 413 and 414 is 170982
Least common multiple can be found by multiplying the highest exponent prime factors of 413 and 414. First we will calculate the prime factors of 413 and 414.
Prime Factorization of 413
| 7 | 413 |
| 59 | 59 |
| 1 |
Prime factors of 413 are 7,59. Prime factorization of 413 in exponential form is:
413 = 71×591
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
Now multiplying the highest exponent prime factors to calculate the LCM of 413 and 414.
LCM(413,414) = 21×32×71×231×591
LCM(413,414) = 170982
Factors of 413
List of positive integer factors of 413 that divides 413 without a remainder.
1, 7, 59, 413
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
Least Common Multiple of 413 and 414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 413 and 414, than apply into the LCM equation.
GCF(413,414) = 1
LCM(413,414) = ( 413 × 414) / 1
LCM(413,414) = 170982 / 1
LCM(413,414) = 170982
Properties of LCM 413 and 414
(i) The LCM of 414 and 413 is associative
LCM of 413 and 414 = LCM of 414 and 413
Related Least Common Multiples of 413
Related Least Common Multiples of 414
Frequently Asked Questions on LCM of 413 and 414
1. What is the LCM of 413 and 414?
Answer: LCM of 413 and 414 is 170982.
2. What are the Factors of 413?
Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.
3. 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.
4. How to Find the LCM of 413 and 414?
Answer:
Least Common Multiple of 413 and 414 = 170982
Step 1: Find the prime factorization of 413
413 = 7 x 59
Step 2: Find the prime factorization of 414
414 = 2 x 3 x 3 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 170982 = 2 x 3 x 3 x 7 x 23 x 59
Step 4: Therefore, the least common multiple of 413 and 414 is 170982.
