Least Common Multiple (LCM) of 193 and 117
The least common multiple (LCM) of 193 and 117 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 193 and 117?
First, calculate the GCD of 193 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 117 = 1 remainder 76 |
| 2 | 117 ÷ 76 = 1 remainder 41 |
| 3 | 76 ÷ 41 = 1 remainder 35 |
| 4 | 41 ÷ 35 = 1 remainder 6 |
| 5 | 35 ÷ 6 = 5 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 19 | 2204 |
| 14 and 14 | 14 |
| 159 and 103 | 16377 |
| 67 and 155 | 10385 |
| 148 and 56 | 2072 |