Least Common Multiple (LCM) of 83 and 142
The least common multiple (LCM) of 83 and 142 is 11786.
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 83 and 142?
First, calculate the GCD of 83 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 142 = 0 remainder 83 |
| 2 | 142 ÷ 83 = 1 remainder 59 |
| 3 | 83 ÷ 59 = 1 remainder 24 |
| 4 | 59 ÷ 24 = 2 remainder 11 |
| 5 | 24 ÷ 11 = 2 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 194 | 12222 |
| 33 and 194 | 6402 |
| 63 and 156 | 3276 |
| 11 and 50 | 550 |
| 195 and 69 | 4485 |