Least Common Multiple (LCM) of 135 and 191
The least common multiple (LCM) of 135 and 191 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 135 and 191?
First, calculate the GCD of 135 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 191 = 0 remainder 135 |
| 2 | 191 ÷ 135 = 1 remainder 56 |
| 3 | 135 ÷ 56 = 2 remainder 23 |
| 4 | 56 ÷ 23 = 2 remainder 10 |
| 5 | 23 ÷ 10 = 2 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 187 | 32164 |
| 16 and 132 | 528 |
| 115 and 67 | 7705 |
| 189 and 120 | 7560 |
| 53 and 62 | 3286 |