Least Common Multiple (LCM) of 116 and 128
The least common multiple (LCM) of 116 and 128 is 3712.
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 116 and 128?
First, calculate the GCD of 116 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 128 = 0 remainder 116 |
| 2 | 128 ÷ 116 = 1 remainder 12 |
| 3 | 116 ÷ 12 = 9 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 107 | 4280 |
| 195 and 25 | 975 |
| 119 and 46 | 5474 |
| 76 and 17 | 1292 |
| 102 and 30 | 510 |