Least Common Multiple (LCM) of 40 and 191
The least common multiple (LCM) of 40 and 191 is 7640.
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 191?
First, calculate the GCD of 40 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 191 = 0 remainder 40 |
| 2 | 191 ÷ 40 = 4 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 |
|---|---|
| 45 and 150 | 450 |
| 122 and 62 | 3782 |
| 25 and 105 | 525 |
| 113 and 24 | 2712 |
| 49 and 109 | 5341 |