Least Common Multiple (LCM) of 82 and 136
The least common multiple (LCM) of 82 and 136 is 5576.
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 136?
First, calculate the GCD of 82 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 136 = 0 remainder 82 |
| 2 | 136 ÷ 82 = 1 remainder 54 |
| 3 | 82 ÷ 54 = 1 remainder 28 |
| 4 | 54 ÷ 28 = 1 remainder 26 |
| 5 | 28 ÷ 26 = 1 remainder 2 |
| 6 | 26 ÷ 2 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 106 | 2756 |
| 12 and 109 | 1308 |
| 119 and 90 | 10710 |
| 103 and 174 | 17922 |
| 164 and 24 | 984 |