Least Common Multiple (LCM) of 199 and 163
The least common multiple (LCM) of 199 and 163 is 32437.
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 199 and 163?
First, calculate the GCD of 199 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 163 = 1 remainder 36 |
| 2 | 163 ÷ 36 = 4 remainder 19 |
| 3 | 36 ÷ 19 = 1 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 116 | 3480 |
| 198 and 192 | 6336 |
| 93 and 153 | 4743 |
| 164 and 125 | 20500 |
| 122 and 157 | 19154 |