Least Common Multiple (LCM) of 117 and 115
The least common multiple (LCM) of 117 and 115 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 117 and 115?
First, calculate the GCD of 117 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 115 = 1 remainder 2 |
| 2 | 115 ÷ 2 = 57 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 52 | 5148 |
| 76 and 162 | 6156 |
| 178 and 53 | 9434 |
| 17 and 96 | 1632 |
| 21 and 45 | 315 |