Least Common Multiple (LCM) of 163 and 105
The least common multiple (LCM) of 163 and 105 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 163 and 105?
First, calculate the GCD of 163 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 105 = 1 remainder 58 |
| 2 | 105 ÷ 58 = 1 remainder 47 |
| 3 | 58 ÷ 47 = 1 remainder 11 |
| 4 | 47 ÷ 11 = 4 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 154 | 1540 |
| 116 and 20 | 580 |
| 142 and 93 | 13206 |
| 25 and 164 | 4100 |
| 120 and 40 | 120 |