Least Common Multiple (LCM) of 199 and 169
The least common multiple (LCM) of 199 and 169 is 33631.
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 169?
First, calculate the GCD of 199 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 169 = 1 remainder 30 |
| 2 | 169 ÷ 30 = 5 remainder 19 |
| 3 | 30 ÷ 19 = 1 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 195 | 2340 |
| 168 and 68 | 2856 |
| 17 and 133 | 2261 |
| 128 and 168 | 2688 |
| 65 and 193 | 12545 |