Least Common Multiple (LCM) of 40 and 45
The least common multiple (LCM) of 40 and 45 is 360.
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 45?
First, calculate the GCD of 40 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 45 = 0 remainder 40 |
| 2 | 45 ÷ 40 = 1 remainder 5 |
| 3 | 40 ÷ 5 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 198 | 11682 |
| 24 and 75 | 600 |
| 190 and 96 | 9120 |
| 15 and 91 | 1365 |
| 30 and 191 | 5730 |