Least Common Multiple (LCM) of 116 and 183
The least common multiple (LCM) of 116 and 183 is 21228.
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 183?
First, calculate the GCD of 116 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 183 = 0 remainder 116 |
| 2 | 183 ÷ 116 = 1 remainder 67 |
| 3 | 116 ÷ 67 = 1 remainder 49 |
| 4 | 67 ÷ 49 = 1 remainder 18 |
| 5 | 49 ÷ 18 = 2 remainder 13 |
| 6 | 18 ÷ 13 = 1 remainder 5 |
| 7 | 13 ÷ 5 = 2 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 96 | 1632 |
| 96 and 27 | 864 |
| 131 and 154 | 20174 |
| 110 and 197 | 21670 |
| 150 and 78 | 1950 |