Least Common Multiple (LCM) of 163 and 107
The least common multiple (LCM) of 163 and 107 is 17441.
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 107?
First, calculate the GCD of 163 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 107 = 1 remainder 56 |
| 2 | 107 ÷ 56 = 1 remainder 51 |
| 3 | 56 ÷ 51 = 1 remainder 5 |
| 4 | 51 ÷ 5 = 10 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 151 | 1510 |
| 85 and 20 | 340 |
| 180 and 32 | 1440 |
| 181 and 91 | 16471 |
| 77 and 106 | 8162 |