Least Common Multiple (LCM) of 115 and 177
The least common multiple (LCM) of 115 and 177 is 20355.
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 177?
First, calculate the GCD of 115 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 177 = 0 remainder 115 |
| 2 | 177 ÷ 115 = 1 remainder 62 |
| 3 | 115 ÷ 62 = 1 remainder 53 |
| 4 | 62 ÷ 53 = 1 remainder 9 |
| 5 | 53 ÷ 9 = 5 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 112 | 14000 |
| 187 and 198 | 3366 |
| 102 and 189 | 6426 |
| 190 and 171 | 1710 |
| 18 and 26 | 234 |