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 |
|---|---|
| 154 and 137 | 21098 |
| 189 and 82 | 15498 |
| 70 and 105 | 210 |
| 36 and 59 | 2124 |
| 106 and 67 | 7102 |