Least Common Multiple (LCM) of 126 and 116
The least common multiple (LCM) of 126 and 116 is 7308.
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 116?
First, calculate the GCD of 126 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 116 = 1 remainder 10 |
| 2 | 116 ÷ 10 = 11 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 89 | 12015 |
| 40 and 197 | 7880 |
| 36 and 39 | 468 |
| 10 and 87 | 870 |
| 128 and 68 | 2176 |