Least Common Multiple of 398 and 403
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 403 the smallest integer that is 160394 that is divisible by both numbers.
Least Common Multiple (LCM) of 398 and 403 is 160394.
LCM(398,403) = 160394
LCM of 398 and 403
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 398 and 403 by Prime method
- Least Common Multiple of 398 and 403 with GCF Formula
LCM of 398 and 403 is 160394
Least common multiple can be found by multiplying the highest exponent prime factors of 398 and 403. First we will calculate the prime factors of 398 and 403.
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 403
| 13 | 403 |
| 31 | 31 |
| 1 |
Prime factors of 403 are 13,31. Prime factorization of 403 in exponential form is:
403 = 131×311
Now multiplying the highest exponent prime factors to calculate the LCM of 398 and 403.
LCM(398,403) = 21×131×311×1991
LCM(398,403) = 160394
Factors of 398
List of positive integer factors of 398 that divides 398 without a remainder.
1, 2, 199, 398
Factors of 403
List of positive integer factors of 403 that divides 403 without a remainder.
1, 13, 31, 403
Least Common Multiple of 398 and 403 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 403, than apply into the LCM equation.
GCF(398,403) = 1
LCM(398,403) = ( 398 × 403) / 1
LCM(398,403) = 160394 / 1
LCM(398,403) = 160394
Properties of LCM 398 and 403
(i) The LCM of 403 and 398 is associative
LCM of 398 and 403 = LCM of 403 and 398
Related Least Common Multiples of 398
Related Least Common Multiples of 403
Frequently Asked Questions on LCM of 398 and 403
1. What is the LCM of 398 and 403?
Answer: LCM of 398 and 403 is 160394.
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 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.
4. How to Find the LCM of 398 and 403?
Answer:
Least Common Multiple of 398 and 403 = 160394
Step 1: Find the prime factorization of 398
398 = 2 x 199
Step 2: Find the prime factorization of 403
403 = 13 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 160394 = 2 x 13 x 31 x 199
Step 4: Therefore, the least common multiple of 398 and 403 is 160394.