Least Common Multiple (LCM) of 40 and 195
The least common multiple (LCM) of 40 and 195 is 1560.
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 195?
First, calculate the GCD of 40 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 195 = 0 remainder 40 |
| 2 | 195 ÷ 40 = 4 remainder 35 |
| 3 | 40 ÷ 35 = 1 remainder 5 |
| 4 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 68 | 6868 |
| 43 and 43 | 43 |
| 18 and 140 | 1260 |
| 16 and 161 | 2576 |
| 69 and 15 | 345 |