Least Common Multiple (LCM) of 40 and 185
The least common multiple (LCM) of 40 and 185 is 1480.
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 185?
First, calculate the GCD of 40 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 185 = 0 remainder 40 |
| 2 | 185 ÷ 40 = 4 remainder 25 |
| 3 | 40 ÷ 25 = 1 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 147 | 1617 |
| 113 and 36 | 4068 |
| 16 and 36 | 144 |
| 79 and 45 | 3555 |
| 16 and 149 | 2384 |