Least Common Multiple (LCM) of 116 and 186
The least common multiple (LCM) of 116 and 186 is 10788.
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 186?
First, calculate the GCD of 116 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 186 = 0 remainder 116 |
| 2 | 186 ÷ 116 = 1 remainder 70 |
| 3 | 116 ÷ 70 = 1 remainder 46 |
| 4 | 70 ÷ 46 = 1 remainder 24 |
| 5 | 46 ÷ 24 = 1 remainder 22 |
| 6 | 24 ÷ 22 = 1 remainder 2 |
| 7 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 120 | 2760 |
| 110 and 115 | 2530 |
| 99 and 10 | 990 |
| 164 and 70 | 5740 |
| 173 and 98 | 16954 |