Least Common Multiple (LCM) of 114 and 40
The least common multiple (LCM) of 114 and 40 is 2280.
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 114 and 40?
First, calculate the GCD of 114 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 40 = 2 remainder 34 |
| 2 | 40 ÷ 34 = 1 remainder 6 |
| 3 | 34 ÷ 6 = 5 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 12 | 516 |
| 153 and 100 | 15300 |
| 119 and 61 | 7259 |
| 102 and 33 | 1122 |
| 175 and 65 | 2275 |