Least Common Multiple (LCM) of 116 and 126
The least common multiple (LCM) of 116 and 126 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 116 and 126?
First, calculate the GCD of 116 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 126 = 0 remainder 116 |
| 2 | 126 ÷ 116 = 1 remainder 10 |
| 3 | 116 ÷ 10 = 11 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 124 | 1240 |
| 78 and 147 | 3822 |
| 157 and 24 | 3768 |
| 81 and 70 | 5670 |
| 195 and 46 | 8970 |