Least Common Multiple of 402 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 402 and 405 the smallest integer that is 54270 that is divisible by both numbers.
Least Common Multiple (LCM) of 402 and 405 is 54270.
LCM(402,405) = 54270
LCM of 402 and 405
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 402 and 405 by Prime method
- Least Common Multiple of 402 and 405 with GCF Formula
LCM of 402 and 405 is 54270
Least common multiple can be found by multiplying the highest exponent prime factors of 402 and 405. First we will calculate the prime factors of 402 and 405.
Prime Factorization of 402
| 2 | 402 |
| 3 | 201 |
| 67 | 67 |
| 1 |
Prime factors of 402 are 2, 3,67. Prime factorization of 402 in exponential form is:
402 = 21×31×671
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 402 and 405.
LCM(402,405) = 21×34×51×671
LCM(402,405) = 54270
Factors of 402
List of positive integer factors of 402 that divides 402 without a remainder.
1, 2, 3, 6, 67, 134, 201, 402
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 402 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 402 and 405, than apply into the LCM equation.
GCF(402,405) = 3
LCM(402,405) = ( 402 × 405) / 3
LCM(402,405) = 162810 / 3
LCM(402,405) = 54270
Properties of LCM 402 and 405
(i) The LCM of 405 and 402 is associative
LCM of 402 and 405 = LCM of 405 and 402
Related Least Common Multiples of 402
Related Least Common Multiples of 405
Frequently Asked Questions on LCM of 402 and 405
1. What is the LCM of 402 and 405?
Answer: LCM of 402 and 405 is 54270.
2. What are the Factors of 402?
Answer: Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402. There are 8 integers that are factors of 402. The greatest factor of 402 is 402.
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 402 and 405?
Answer:
Least Common Multiple of 402 and 405 = 54270
Step 1: Find the prime factorization of 402
402 = 2 x 3 x 67
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 = 54270 = 2 x 3 x 3 x 3 x 3 x 5 x 67
Step 4: Therefore, the least common multiple of 402 and 405 is 54270.