Least Common Multiple (LCM) of 82 and 135
The least common multiple (LCM) of 82 and 135 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 82 and 135?
First, calculate the GCD of 82 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 135 = 0 remainder 82 |
| 2 | 135 ÷ 82 = 1 remainder 53 |
| 3 | 82 ÷ 53 = 1 remainder 29 |
| 4 | 53 ÷ 29 = 1 remainder 24 |
| 5 | 29 ÷ 24 = 1 remainder 5 |
| 6 | 24 ÷ 5 = 4 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 102 | 1122 |
| 123 and 84 | 3444 |
| 103 and 117 | 12051 |
| 138 and 107 | 14766 |
| 95 and 108 | 10260 |