Least Common Multiple (LCM) of 116 and 182
The least common multiple (LCM) of 116 and 182 is 10556.
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 182?
First, calculate the GCD of 116 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 182 = 0 remainder 116 |
| 2 | 182 ÷ 116 = 1 remainder 66 |
| 3 | 116 ÷ 66 = 1 remainder 50 |
| 4 | 66 ÷ 50 = 1 remainder 16 |
| 5 | 50 ÷ 16 = 3 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 80 | 1680 |
| 54 and 59 | 3186 |
| 152 and 170 | 12920 |
| 25 and 106 | 2650 |
| 77 and 70 | 770 |