Least Common Multiple of 398 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 398 and 405 the smallest integer that is 161190 that is divisible by both numbers.
Least Common Multiple (LCM) of 398 and 405 is 161190.
LCM(398,405) = 161190
LCM of 398 and 405
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 398 and 405 by Prime method
- Least Common Multiple of 398 and 405 with GCF Formula
LCM of 398 and 405 is 161190
Least common multiple can be found by multiplying the highest exponent prime factors of 398 and 405. First we will calculate the prime factors of 398 and 405.
Prime Factorization of 398
| 2 | 398 |
| 199 | 199 |
| 1 |
Prime factors of 398 are 2,199. Prime factorization of 398 in exponential form is:
398 = 21×1991
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 398 and 405.
LCM(398,405) = 21×34×51×1991
LCM(398,405) = 161190
Factors of 398
List of positive integer factors of 398 that divides 398 without a remainder.
1, 2, 199, 398
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 398 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 398 and 405, than apply into the LCM equation.
GCF(398,405) = 1
LCM(398,405) = ( 398 × 405) / 1
LCM(398,405) = 161190 / 1
LCM(398,405) = 161190
Properties of LCM 398 and 405
(i) The LCM of 405 and 398 is associative
LCM of 398 and 405 = LCM of 405 and 398
Related Least Common Multiples of 398
Related Least Common Multiples of 405
Frequently Asked Questions on LCM of 398 and 405
1. What is the LCM of 398 and 405?
Answer: LCM of 398 and 405 is 161190.
2. What are the Factors of 398?
Answer: Factors of 398 are 1, 2, 199, 398. There are 4 integers that are factors of 398. The greatest factor of 398 is 398.
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 398 and 405?
Answer:
Least Common Multiple of 398 and 405 = 161190
Step 1: Find the prime factorization of 398
398 = 2 x 199
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 = 161190 = 2 x 3 x 3 x 3 x 3 x 5 x 199
Step 4: Therefore, the least common multiple of 398 and 405 is 161190.