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 |
|---|---|
| 165 and 81 | 4455 |
| 176 and 165 | 2640 |
| 119 and 69 | 8211 |
| 29 and 163 | 4727 |
| 160 and 100 | 800 |