Least Common Multiple (LCM) of 40 and 186
The least common multiple (LCM) of 40 and 186 is 3720.
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 186?
First, calculate the GCD of 40 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 186 = 0 remainder 40 |
| 2 | 186 ÷ 40 = 4 remainder 26 |
| 3 | 40 ÷ 26 = 1 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 162 | 10530 |
| 177 and 65 | 11505 |
| 17 and 16 | 272 |
| 31 and 127 | 3937 |
| 43 and 167 | 7181 |