Least Common Multiple (LCM) of 163 and 192
The least common multiple (LCM) of 163 and 192 is 31296.
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 192?
First, calculate the GCD of 163 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 192 = 0 remainder 163 |
| 2 | 192 ÷ 163 = 1 remainder 29 |
| 3 | 163 ÷ 29 = 5 remainder 18 |
| 4 | 29 ÷ 18 = 1 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 131 | 11921 |
| 167 and 48 | 8016 |
| 84 and 42 | 84 |
| 68 and 180 | 3060 |
| 21 and 192 | 1344 |