Least Common Multiple (LCM) of 40 and 145
The least common multiple (LCM) of 40 and 145 is 1160.
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 145?
First, calculate the GCD of 40 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 145 = 0 remainder 40 |
| 2 | 145 ÷ 40 = 3 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 |
|---|---|
| 105 and 122 | 12810 |
| 54 and 42 | 378 |
| 53 and 12 | 636 |
| 16 and 28 | 112 |
| 131 and 200 | 26200 |