Least Common Multiple (LCM) of 115 and 192
The least common multiple (LCM) of 115 and 192 is 22080.
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 192?
First, calculate the GCD of 115 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 192 = 0 remainder 115 |
| 2 | 192 ÷ 115 = 1 remainder 77 |
| 3 | 115 ÷ 77 = 1 remainder 38 |
| 4 | 77 ÷ 38 = 2 remainder 1 |
| 5 | 38 ÷ 1 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 45 | 360 |
| 176 and 33 | 528 |
| 157 and 135 | 21195 |
| 108 and 133 | 14364 |
| 125 and 167 | 20875 |