Least Common Multiple (LCM) of 126 and 83
The least common multiple (LCM) of 126 and 83 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 126 and 83?
First, calculate the GCD of 126 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 83 = 1 remainder 43 |
| 2 | 83 ÷ 43 = 1 remainder 40 |
| 3 | 43 ÷ 40 = 1 remainder 3 |
| 4 | 40 ÷ 3 = 13 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 33 | 4785 |
| 133 and 172 | 22876 |
| 92 and 21 | 1932 |
| 149 and 36 | 5364 |
| 103 and 65 | 6695 |