Least Common Multiple (LCM) of 105 and 163
The least common multiple (LCM) of 105 and 163 is 17115.
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 105 and 163?
First, calculate the GCD of 105 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 163 = 0 remainder 105 |
| 2 | 163 ÷ 105 = 1 remainder 58 |
| 3 | 105 ÷ 58 = 1 remainder 47 |
| 4 | 58 ÷ 47 = 1 remainder 11 |
| 5 | 47 ÷ 11 = 4 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 157 | 8635 |
| 94 and 98 | 4606 |
| 50 and 159 | 7950 |
| 114 and 63 | 2394 |
| 21 and 56 | 168 |