Least Common Multiple (LCM) of 115 and 68
The least common multiple (LCM) of 115 and 68 is 7820.
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 68?
First, calculate the GCD of 115 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 68 = 1 remainder 47 |
| 2 | 68 ÷ 47 = 1 remainder 21 |
| 3 | 47 ÷ 21 = 2 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 65 | 12090 |
| 119 and 69 | 8211 |
| 173 and 84 | 14532 |
| 73 and 101 | 7373 |
| 36 and 129 | 1548 |