Least Common Multiple of 403 and 405
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 403 and 405 the smallest integer that is 163215 that is divisible by both numbers.
Least Common Multiple (LCM) of 403 and 405 is 163215.
LCM(403,405) = 163215
LCM of 403 and 405
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 403 and 405 by Prime method
- Least Common Multiple of 403 and 405 with GCF Formula
LCM of 403 and 405 is 163215
Least common multiple can be found by multiplying the highest exponent prime factors of 403 and 405. First we will calculate the prime factors of 403 and 405.
Prime Factorization of 403
| 13 | 403 |
| 31 | 31 |
| 1 |
Prime factors of 403 are 13,31. Prime factorization of 403 in exponential form is:
403 = 131×311
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
Now multiplying the highest exponent prime factors to calculate the LCM of 403 and 405.
LCM(403,405) = 34×51×131×311
LCM(403,405) = 163215
Factors of 403
List of positive integer factors of 403 that divides 403 without a remainder.
1, 13, 31, 403
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
Least Common Multiple of 403 and 405 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 403 and 405, than apply into the LCM equation.
GCF(403,405) = 1
LCM(403,405) = ( 403 × 405) / 1
LCM(403,405) = 163215 / 1
LCM(403,405) = 163215
Properties of LCM 403 and 405
(i) The LCM of 405 and 403 is associative
LCM of 403 and 405 = LCM of 405 and 403
Related Least Common Multiples of 403
Related Least Common Multiples of 405
Frequently Asked Questions on LCM of 403 and 405
1. What is the LCM of 403 and 405?
Answer: LCM of 403 and 405 is 163215.
2. What are the Factors of 403?
Answer: Factors of 403 are 1, 13, 31, 403. There are 4 integers that are factors of 403. The greatest factor of 403 is 403.
3. 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.
4. How to Find the LCM of 403 and 405?
Answer:
Least Common Multiple of 403 and 405 = 163215
Step 1: Find the prime factorization of 403
403 = 13 x 31
Step 2: Find the prime factorization of 405
405 = 3 x 3 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 163215 = 3 x 3 x 3 x 3 x 5 x 13 x 31
Step 4: Therefore, the least common multiple of 403 and 405 is 163215.
