Least Common Multiple (LCM) of 117 and 194
The least common multiple (LCM) of 117 and 194 is 22698.
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 194?
First, calculate the GCD of 117 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 194 = 0 remainder 117 |
| 2 | 194 ÷ 117 = 1 remainder 77 |
| 3 | 117 ÷ 77 = 1 remainder 40 |
| 4 | 77 ÷ 40 = 1 remainder 37 |
| 5 | 40 ÷ 37 = 1 remainder 3 |
| 6 | 37 ÷ 3 = 12 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 47 | 1692 |
| 66 and 18 | 198 |
| 176 and 129 | 22704 |
| 142 and 90 | 6390 |
| 137 and 194 | 26578 |