Least Common Multiple (LCM) of 117 and 163
The least common multiple (LCM) of 117 and 163 is 19071.
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 163?
First, calculate the GCD of 117 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 163 = 0 remainder 117 |
| 2 | 163 ÷ 117 = 1 remainder 46 |
| 3 | 117 ÷ 46 = 2 remainder 25 |
| 4 | 46 ÷ 25 = 1 remainder 21 |
| 5 | 25 ÷ 21 = 1 remainder 4 |
| 6 | 21 ÷ 4 = 5 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 36 | 1764 |
| 106 and 46 | 2438 |
| 61 and 81 | 4941 |
| 71 and 178 | 12638 |
| 181 and 115 | 20815 |