Least Common Multiple (LCM) of 40 and 111
The least common multiple (LCM) of 40 and 111 is 4440.
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 40 and 111?
First, calculate the GCD of 40 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 111 = 0 remainder 40 |
| 2 | 111 ÷ 40 = 2 remainder 31 |
| 3 | 40 ÷ 31 = 1 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 109 | 4687 |
| 99 and 29 | 2871 |
| 91 and 71 | 6461 |
| 138 and 174 | 4002 |
| 189 and 144 | 3024 |