Least Common Multiple (LCM) of 191 and 135
The least common multiple (LCM) of 191 and 135 is 25785.
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 191 and 135?
First, calculate the GCD of 191 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 135 = 1 remainder 56 |
| 2 | 135 ÷ 56 = 2 remainder 23 |
| 3 | 56 ÷ 23 = 2 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 107 | 14231 |
| 140 and 54 | 3780 |
| 123 and 127 | 15621 |
| 84 and 100 | 2100 |
| 101 and 159 | 16059 |