Least Common Multiple (LCM) of 115 and 137
The least common multiple (LCM) of 115 and 137 is 15755.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 115 and 137?
First, calculate the GCD of 115 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 137 = 0 remainder 115 |
| 2 | 137 ÷ 115 = 1 remainder 22 |
| 3 | 115 ÷ 22 = 5 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 13 | 1300 |
| 82 and 44 | 1804 |
| 131 and 89 | 11659 |
| 159 and 15 | 795 |
| 121 and 77 | 847 |