Least Common Multiple (LCM) of 125 and 82
The least common multiple (LCM) of 125 and 82 is 10250.
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 125 and 82?
First, calculate the GCD of 125 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 82 = 1 remainder 43 |
| 2 | 82 ÷ 43 = 1 remainder 39 |
| 3 | 43 ÷ 39 = 1 remainder 4 |
| 4 | 39 ÷ 4 = 9 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 84 | 420 |
| 195 and 54 | 3510 |
| 130 and 21 | 2730 |
| 86 and 185 | 15910 |
| 42 and 121 | 5082 |