Least Common Multiple of 400 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 400 and 405 the smallest integer that is 32400 that is divisible by both numbers.
Least Common Multiple (LCM) of 400 and 405 is 32400.
LCM(400,405) = 32400
LCM of 400 and 405
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 400 and 405 by Prime method
- Least Common Multiple of 400 and 405 with GCF Formula
LCM of 400 and 405 is 32400
Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 405. First we will calculate the prime factors of 400 and 405.
Prime Factorization of 400
| 2 | 400 |
| 2 | 200 |
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 400 are 2,5. Prime factorization of 400 in exponential form is:
400 = 24×52
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 400 and 405.
LCM(400,405) = 24×34×52
LCM(400,405) = 32400
Factors of 400
List of positive integer factors of 400 that divides 400 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
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 400 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 400 and 405, than apply into the LCM equation.
GCF(400,405) = 5
LCM(400,405) = ( 400 × 405) / 5
LCM(400,405) = 162000 / 5
LCM(400,405) = 32400
Properties of LCM 400 and 405
(i) The LCM of 405 and 400 is associative
LCM of 400 and 405 = LCM of 405 and 400
Related Least Common Multiples of 400
Related Least Common Multiples of 405
Frequently Asked Questions on LCM of 400 and 405
1. What is the LCM of 400 and 405?
Answer: LCM of 400 and 405 is 32400.
2. What are the Factors of 400?
Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.
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 400 and 405?
Answer:
Least Common Multiple of 400 and 405 = 32400
Step 1: Find the prime factorization of 400
400 = 2 x 2 x 2 x 2 x 5 x 5
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 = 32400 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 400 and 405 is 32400.
