Least Common Multiple (LCM) of 115 and 45
The least common multiple (LCM) of 115 and 45 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 115 and 45?
First, calculate the GCD of 115 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 45 = 2 remainder 25 |
| 2 | 45 ÷ 25 = 1 remainder 20 |
| 3 | 25 ÷ 20 = 1 remainder 5 |
| 4 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 101 | 4545 |
| 68 and 33 | 2244 |
| 31 and 147 | 4557 |
| 168 and 195 | 10920 |
| 105 and 23 | 2415 |