Least Common Multiple (LCM) of 115 and 176
The least common multiple (LCM) of 115 and 176 is 20240.
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 176?
First, calculate the GCD of 115 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 176 = 0 remainder 115 |
| 2 | 176 ÷ 115 = 1 remainder 61 |
| 3 | 115 ÷ 61 = 1 remainder 54 |
| 4 | 61 ÷ 54 = 1 remainder 7 |
| 5 | 54 ÷ 7 = 7 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 162 | 1134 |
| 88 and 172 | 3784 |
| 121 and 138 | 16698 |
| 80 and 188 | 3760 |
| 188 and 50 | 4700 |