Least Common Multiple (LCM) of 115 and 117
The least common multiple (LCM) of 115 and 117 is 13455.
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 117?
First, calculate the GCD of 115 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 117 = 0 remainder 115 |
| 2 | 117 ÷ 115 = 1 remainder 2 |
| 3 | 115 ÷ 2 = 57 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 197 | 32505 |
| 60 and 149 | 8940 |
| 124 and 88 | 2728 |
| 37 and 120 | 4440 |
| 102 and 84 | 1428 |