Least Common Multiple (LCM) of 135 and 197
The least common multiple (LCM) of 135 and 197 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 135 and 197?
First, calculate the GCD of 135 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 197 = 0 remainder 135 |
| 2 | 197 ÷ 135 = 1 remainder 62 |
| 3 | 135 ÷ 62 = 2 remainder 11 |
| 4 | 62 ÷ 11 = 5 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 73 | 5840 |
| 191 and 77 | 14707 |
| 137 and 69 | 9453 |
| 70 and 141 | 9870 |
| 35 and 15 | 105 |