Least Common Multiple (LCM) of 135 and 82
The least common multiple (LCM) of 135 and 82 is 11070.
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 82?
First, calculate the GCD of 135 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 82 = 1 remainder 53 |
| 2 | 82 ÷ 53 = 1 remainder 29 |
| 3 | 53 ÷ 29 = 1 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 116 | 1972 |
| 68 and 100 | 1700 |
| 71 and 170 | 12070 |
| 148 and 193 | 28564 |
| 75 and 35 | 525 |