Least Common Multiple (LCM) of 40 and 199
The least common multiple (LCM) of 40 and 199 is 7960.
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 199?
First, calculate the GCD of 40 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 199 = 0 remainder 40 |
| 2 | 199 ÷ 40 = 4 remainder 39 |
| 3 | 40 ÷ 39 = 1 remainder 1 |
| 4 | 39 ÷ 1 = 39 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 175 | 2800 |
| 54 and 37 | 1998 |
| 117 and 172 | 20124 |
| 65 and 13 | 65 |
| 136 and 43 | 5848 |