Least Common Multiple (LCM) of 142 and 82
The least common multiple (LCM) of 142 and 82 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 142 and 82?
First, calculate the GCD of 142 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 82 = 1 remainder 60 |
| 2 | 82 ÷ 60 = 1 remainder 22 |
| 3 | 60 ÷ 22 = 2 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 123 | 5412 |
| 200 and 36 | 1800 |
| 82 and 183 | 15006 |
| 162 and 48 | 1296 |
| 189 and 89 | 16821 |