Least Common Multiple (LCM) of 43 and 105
The least common multiple (LCM) of 43 and 105 is 4515.
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 105?
First, calculate the GCD of 43 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 105 = 0 remainder 43 |
| 2 | 105 ÷ 43 = 2 remainder 19 |
| 3 | 43 ÷ 19 = 2 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 81 | 8343 |
| 51 and 135 | 2295 |
| 142 and 87 | 12354 |
| 23 and 141 | 3243 |
| 128 and 200 | 3200 |