Least Common Multiple (LCM) of 163 and 194
The least common multiple (LCM) of 163 and 194 is 31622.
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 194?
First, calculate the GCD of 163 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 194 = 0 remainder 163 |
| 2 | 194 ÷ 163 = 1 remainder 31 |
| 3 | 163 ÷ 31 = 5 remainder 8 |
| 4 | 31 ÷ 8 = 3 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 179 | 19332 |
| 182 and 23 | 4186 |
| 181 and 105 | 19005 |
| 16 and 109 | 1744 |
| 111 and 116 | 12876 |