Least Common Multiple (LCM) of 115 and 160
The least common multiple (LCM) of 115 and 160 is 3680.
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 160?
First, calculate the GCD of 115 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 160 = 0 remainder 115 |
| 2 | 160 ÷ 115 = 1 remainder 45 |
| 3 | 115 ÷ 45 = 2 remainder 25 |
| 4 | 45 ÷ 25 = 1 remainder 20 |
| 5 | 25 ÷ 20 = 1 remainder 5 |
| 6 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 67 | 11926 |
| 34 and 102 | 102 |
| 68 and 71 | 4828 |
| 17 and 138 | 2346 |
| 123 and 185 | 22755 |