Least Common Multiple (LCM) of 83 and 126
The least common multiple (LCM) of 83 and 126 is 10458.
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 126?
First, calculate the GCD of 83 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 126 = 0 remainder 83 |
| 2 | 126 ÷ 83 = 1 remainder 43 |
| 3 | 83 ÷ 43 = 1 remainder 40 |
| 4 | 43 ÷ 40 = 1 remainder 3 |
| 5 | 40 ÷ 3 = 13 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 186 | 1860 |
| 59 and 62 | 3658 |
| 178 and 188 | 16732 |
| 101 and 126 | 12726 |
| 128 and 112 | 896 |