Least Common Multiple of 338 and 345
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 338 and 345 the smallest integer that is 116610 that is divisible by both numbers.
Least Common Multiple (LCM) of 338 and 345 is 116610.
LCM(338,345) = 116610
LCM of 338 and 345
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 338 and 345 by Prime method
- Least Common Multiple of 338 and 345 with GCF Formula
LCM of 338 and 345 is 116610
Least common multiple can be found by multiplying the highest exponent prime factors of 338 and 345. First we will calculate the prime factors of 338 and 345.
Prime Factorization of 338
| 2 | 338 |
| 13 | 169 |
| 13 | 13 |
| 1 |
Prime factors of 338 are 2,13. Prime factorization of 338 in exponential form is:
338 = 21×132
Prime Factorization of 345
| 3 | 345 |
| 5 | 115 |
| 23 | 23 |
| 1 |
Prime factors of 345 are 3, 5,23. Prime factorization of 345 in exponential form is:
345 = 31×51×231
Now multiplying the highest exponent prime factors to calculate the LCM of 338 and 345.
LCM(338,345) = 21×31×51×132×231
LCM(338,345) = 116610
Factors of 338
List of positive integer factors of 338 that divides 338 without a remainder.
1, 2, 13, 26, 169, 338
Factors of 345
List of positive integer factors of 345 that divides 345 without a remainder.
1, 3, 5, 15, 23, 69, 115, 345
Least Common Multiple of 338 and 345 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 338 and 345, than apply into the LCM equation.
GCF(338,345) = 1
LCM(338,345) = ( 338 × 345) / 1
LCM(338,345) = 116610 / 1
LCM(338,345) = 116610
Properties of LCM 338 and 345
(i) The LCM of 345 and 338 is associative
LCM of 338 and 345 = LCM of 345 and 338
Related Least Common Multiples of 338
Related Least Common Multiples of 345
Frequently Asked Questions on LCM of 338 and 345
1. What is the LCM of 338 and 345?
Answer: LCM of 338 and 345 is 116610.
2. What are the Factors of 338?
Answer: Factors of 338 are 1, 2, 13, 26, 169, 338. There are 6 integers that are factors of 338. The greatest factor of 338 is 338.
3. What are the Factors of 345?
Answer: Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345. There are 8 integers that are factors of 345. The greatest factor of 345 is 345.
4. How to Find the LCM of 338 and 345?
Answer:
Least Common Multiple of 338 and 345 = 116610
Step 1: Find the prime factorization of 338
338 = 2 x 13 x 13
Step 2: Find the prime factorization of 345
345 = 3 x 5 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 116610 = 2 x 3 x 5 x 13 x 13 x 23
Step 4: Therefore, the least common multiple of 338 and 345 is 116610.
