Least Common Multiple (LCM) of 169 and 194
The least common multiple (LCM) of 169 and 194 is 32786.
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 169 and 194?
First, calculate the GCD of 169 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 194 = 0 remainder 169 |
| 2 | 194 ÷ 169 = 1 remainder 25 |
| 3 | 169 ÷ 25 = 6 remainder 19 |
| 4 | 25 ÷ 19 = 1 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 195 | 13065 |
| 59 and 150 | 8850 |
| 54 and 71 | 3834 |
| 71 and 144 | 10224 |
| 173 and 71 | 12283 |