Least Common Multiple (LCM) of 116 and 181
The least common multiple (LCM) of 116 and 181 is 20996.
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 181?
First, calculate the GCD of 116 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 181 = 0 remainder 116 |
| 2 | 181 ÷ 116 = 1 remainder 65 |
| 3 | 116 ÷ 65 = 1 remainder 51 |
| 4 | 65 ÷ 51 = 1 remainder 14 |
| 5 | 51 ÷ 14 = 3 remainder 9 |
| 6 | 14 ÷ 9 = 1 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 155 | 5115 |
| 28 and 163 | 4564 |
| 190 and 172 | 16340 |
| 100 and 139 | 13900 |
| 168 and 42 | 168 |