Least Common Multiple (LCM) of 116 and 193
The least common multiple (LCM) of 116 and 193 is 22388.
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 193?
First, calculate the GCD of 116 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 193 = 0 remainder 116 |
| 2 | 193 ÷ 116 = 1 remainder 77 |
| 3 | 116 ÷ 77 = 1 remainder 39 |
| 4 | 77 ÷ 39 = 1 remainder 38 |
| 5 | 39 ÷ 38 = 1 remainder 1 |
| 6 | 38 ÷ 1 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 178 | 2314 |
| 85 and 140 | 2380 |
| 49 and 180 | 8820 |
| 50 and 56 | 1400 |
| 15 and 144 | 720 |