Least Common Multiple (LCM) of 116 and 177
The least common multiple (LCM) of 116 and 177 is 20532.
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 177?
First, calculate the GCD of 116 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 177 = 0 remainder 116 |
| 2 | 177 ÷ 116 = 1 remainder 61 |
| 3 | 116 ÷ 61 = 1 remainder 55 |
| 4 | 61 ÷ 55 = 1 remainder 6 |
| 5 | 55 ÷ 6 = 9 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 88 | 3432 |
| 119 and 147 | 2499 |
| 132 and 196 | 6468 |
| 46 and 186 | 4278 |
| 80 and 88 | 880 |