Least Common Multiple (LCM) of 115 and 128
The least common multiple (LCM) of 115 and 128 is 14720.
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 128?
First, calculate the GCD of 115 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 128 = 0 remainder 115 |
| 2 | 128 ÷ 115 = 1 remainder 13 |
| 3 | 115 ÷ 13 = 8 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 29 | 609 |
| 144 and 165 | 7920 |
| 158 and 92 | 7268 |
| 140 and 68 | 2380 |
| 199 and 101 | 20099 |