Least Common Multiple (LCM) of 69 and 82
The least common multiple (LCM) of 69 and 82 is 5658.
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 69 and 82?
First, calculate the GCD of 69 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 82 = 0 remainder 69 |
| 2 | 82 ÷ 69 = 1 remainder 13 |
| 3 | 69 ÷ 13 = 5 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 156 | 3588 |
| 82 and 56 | 2296 |
| 105 and 200 | 4200 |
| 21 and 31 | 651 |
| 142 and 174 | 12354 |