Least Common Multiple (LCM) of 43 and 115
The least common multiple (LCM) of 43 and 115 is 4945.
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 43 and 115?
First, calculate the GCD of 43 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 115 = 0 remainder 43 |
| 2 | 115 ÷ 43 = 2 remainder 29 |
| 3 | 43 ÷ 29 = 1 remainder 14 |
| 4 | 29 ÷ 14 = 2 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 22 | 1650 |
| 100 and 104 | 2600 |
| 10 and 105 | 210 |
| 199 and 173 | 34427 |
| 170 and 68 | 340 |