Least Common Multiple (LCM) of 82 and 145
The least common multiple (LCM) of 82 and 145 is 11890.
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 145?
First, calculate the GCD of 82 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 145 = 0 remainder 82 |
| 2 | 145 ÷ 82 = 1 remainder 63 |
| 3 | 82 ÷ 63 = 1 remainder 19 |
| 4 | 63 ÷ 19 = 3 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 174 | 174 |
| 100 and 45 | 900 |
| 10 and 125 | 250 |
| 22 and 32 | 352 |
| 176 and 156 | 6864 |