Least Common Multiple (LCM) of 117 and 193
The least common multiple (LCM) of 117 and 193 is 22581.
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 117 and 193?
First, calculate the GCD of 117 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 193 = 0 remainder 117 |
| 2 | 193 ÷ 117 = 1 remainder 76 |
| 3 | 117 ÷ 76 = 1 remainder 41 |
| 4 | 76 ÷ 41 = 1 remainder 35 |
| 5 | 41 ÷ 35 = 1 remainder 6 |
| 6 | 35 ÷ 6 = 5 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 39 | 1287 |
| 43 and 13 | 559 |
| 79 and 136 | 10744 |
| 172 and 32 | 1376 |
| 38 and 102 | 1938 |