Least Common Multiple (LCM) of 45 and 115
The least common multiple (LCM) of 45 and 115 is 1035.
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 45 and 115?
First, calculate the GCD of 45 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 115 = 0 remainder 45 |
| 2 | 115 ÷ 45 = 2 remainder 25 |
| 3 | 45 ÷ 25 = 1 remainder 20 |
| 4 | 25 ÷ 20 = 1 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 30 | 2580 |
| 54 and 181 | 9774 |
| 75 and 105 | 525 |
| 71 and 20 | 1420 |
| 40 and 111 | 4440 |