Least Common Multiple of 405 and 413
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 405 and 413 the smallest integer that is 167265 that is divisible by both numbers.
Least Common Multiple (LCM) of 405 and 413 is 167265.
LCM(405,413) = 167265
LCM of 405 and 413
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 405 and 413 by Prime method
- Least Common Multiple of 405 and 413 with GCF Formula
LCM of 405 and 413 is 167265
Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 413. First we will calculate the prime factors of 405 and 413.
Prime Factorization of 405
| 3 | 405 |
| 3 | 135 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 405 are 3,5. Prime factorization of 405 in exponential form is:
405 = 34×51
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
Now multiplying the highest exponent prime factors to calculate the LCM of 405 and 413.
LCM(405,413) = 34×51×71×591
LCM(405,413) = 167265
Factors of 405
List of positive integer factors of 405 that divides 405 without a remainder.
1, 3, 5, 9, 15, 27, 45, 81, 135, 405
Factors of 413
List of positive integer factors of 413 that divides 413 without a remainder.
1, 7, 59, 413
Least Common Multiple of 405 and 413 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 405 and 413, than apply into the LCM equation.
GCF(405,413) = 1
LCM(405,413) = ( 405 × 413) / 1
LCM(405,413) = 167265 / 1
LCM(405,413) = 167265
Properties of LCM 405 and 413
(i) The LCM of 413 and 405 is associative
LCM of 405 and 413 = LCM of 413 and 405
Related Least Common Multiples of 405
Related Least Common Multiples of 413
Frequently Asked Questions on LCM of 405 and 413
1. What is the LCM of 405 and 413?
Answer: LCM of 405 and 413 is 167265.
2. What are the Factors of 405?
Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.
3. 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.
4. How to Find the LCM of 405 and 413?
Answer:
Least Common Multiple of 405 and 413 = 167265
Step 1: Find the prime factorization of 405
405 = 3 x 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 413
413 = 7 x 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 167265 = 3 x 3 x 3 x 3 x 5 x 7 x 59
Step 4: Therefore, the least common multiple of 405 and 413 is 167265.