Least Common Multiple (LCM) of 82 and 25
The least common multiple (LCM) of 82 and 25 is 2050.
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 25?
First, calculate the GCD of 82 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 25 = 3 remainder 7 |
| 2 | 25 ÷ 7 = 3 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 98 | 2842 |
| 20 and 46 | 460 |
| 20 and 28 | 140 |
| 90 and 118 | 5310 |
| 42 and 57 | 798 |