Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 26315 and 26320 the smallest integer that is 138522160 that is divisible by both numbers.
Least Common Multiple (LCM) of 26315 and 26320 is 138522160.
LCM(26315,26320) = 138522160
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 26315 and 26320. First we will calculate the prime factors of 26315 and 26320.
Prime Factorization of 26315
5 | 26315 |
19 | 5263 |
277 | 277 |
1 |
Prime factors of 26315 are 5, 19,277. Prime factorization of 26315 in exponential form is:
26315 = 51×191×2771
Prime Factorization of 26320
2 | 26320 |
2 | 13160 |
2 | 6580 |
2 | 3290 |
5 | 1645 |
7 | 329 |
47 | 47 |
1 |
Prime factors of 26320 are 2, 5, 7,47. Prime factorization of 26320 in exponential form is:
26320 = 24×51×71×471
Now multiplying the highest exponent prime factors to calculate the LCM of 26315 and 26320.
LCM(26315,26320) = 24×51×71×191×471×2771
LCM(26315,26320) = 138522160
Factors of 26315
List of positive integer factors of 26315 that divides 26315 without a remainder.
1, 5, 19, 95, 277, 1385, 5263, 26315
Factors of 26320
List of positive integer factors of 26320 that divides 26320 without a remainder.
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 47, 56, 70, 80, 94, 112, 140, 188, 235, 280, 329, 376, 470, 560, 658, 752, 940, 1316, 1645, 1880, 2632, 3290, 3760, 5264, 6580, 13160, 26320
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26315 and 26320, than apply into the LCM equation.
GCF(26315,26320) = 5
LCM(26315,26320) = ( 26315 × 26320) / 5
LCM(26315,26320) = 692610800 / 5
LCM(26315,26320) = 138522160
(i) The LCM of 26320 and 26315 is associative
LCM of 26315 and 26320 = LCM of 26320 and 26315
1. What is the LCM of 26315 and 26320?
Answer: LCM of 26315 and 26320 is 138522160.
2. What are the Factors of 26315?
Answer: Factors of 26315 are 1, 5, 19, 95, 277, 1385, 5263, 26315. There are 8 integers that are factors of 26315. The greatest factor of 26315 is 26315.
3. What are the Factors of 26320?
Answer: Factors of 26320 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 47, 56, 70, 80, 94, 112, 140, 188, 235, 280, 329, 376, 470, 560, 658, 752, 940, 1316, 1645, 1880, 2632, 3290, 3760, 5264, 6580, 13160, 26320. There are 40 integers that are factors of 26320. The greatest factor of 26320 is 26320.
4. How to Find the LCM of 26315 and 26320?
Answer:
Least Common Multiple of 26315 and 26320 = 138522160
Step 1: Find the prime factorization of 26315
26315 = 5 x 19 x 277
Step 2: Find the prime factorization of 26320
26320 = 2 x 2 x 2 x 2 x 5 x 7 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 138522160 = 2 x 2 x 2 x 2 x 5 x 7 x 19 x 47 x 277
Step 4: Therefore, the least common multiple of 26315 and 26320 is 138522160.