Least Common Multiple (LCM) of 116 and 40
The least common multiple (LCM) of 116 and 40 is 1160.
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 40?
First, calculate the GCD of 116 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 40 = 2 remainder 36 |
| 2 | 40 ÷ 36 = 1 remainder 4 |
| 3 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 196 | 392 |
| 148 and 185 | 740 |
| 105 and 45 | 315 |
| 72 and 107 | 7704 |
| 132 and 89 | 11748 |