Least Common Multiple (LCM) of 82 and 142
The least common multiple (LCM) of 82 and 142 is 5822.
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 142?
First, calculate the GCD of 82 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 142 = 0 remainder 82 |
| 2 | 142 ÷ 82 = 1 remainder 60 |
| 3 | 82 ÷ 60 = 1 remainder 22 |
| 4 | 60 ÷ 22 = 2 remainder 16 |
| 5 | 22 ÷ 16 = 1 remainder 6 |
| 6 | 16 ÷ 6 = 2 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 20 | 3820 |
| 98 and 165 | 16170 |
| 10 and 198 | 990 |
| 105 and 169 | 17745 |
| 37 and 20 | 740 |