Least Common Multiple (LCM) of 197 and 135
The least common multiple (LCM) of 197 and 135 is 26595.
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 197 and 135?
First, calculate the GCD of 197 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 135 = 1 remainder 62 |
| 2 | 135 ÷ 62 = 2 remainder 11 |
| 3 | 62 ÷ 11 = 5 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 10 | 960 |
| 13 and 120 | 1560 |
| 39 and 34 | 1326 |
| 50 and 137 | 6850 |
| 90 and 84 | 1260 |