Least Common Multiple (LCM) of 163 and 191
The least common multiple (LCM) of 163 and 191 is 31133.
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 191?
First, calculate the GCD of 163 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 191 = 0 remainder 163 |
| 2 | 191 ÷ 163 = 1 remainder 28 |
| 3 | 163 ÷ 28 = 5 remainder 23 |
| 4 | 28 ÷ 23 = 1 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 46 | 2300 |
| 43 and 96 | 4128 |
| 164 and 17 | 2788 |
| 32 and 106 | 1696 |
| 31 and 129 | 3999 |