Least Common Multiple (LCM) of 82 and 97
The least common multiple (LCM) of 82 and 97 is 7954.
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 97?
First, calculate the GCD of 82 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 97 = 0 remainder 82 |
| 2 | 97 ÷ 82 = 1 remainder 15 |
| 3 | 82 ÷ 15 = 5 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 177 | 17700 |
| 90 and 120 | 360 |
| 107 and 23 | 2461 |
| 112 and 143 | 16016 |
| 100 and 32 | 800 |