Least Common Multiple (LCM) of 43 and 75
The least common multiple (LCM) of 43 and 75 is 3225.
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 75?
First, calculate the GCD of 43 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 75 = 0 remainder 43 |
| 2 | 75 ÷ 43 = 1 remainder 32 |
| 3 | 43 ÷ 32 = 1 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 11 | 352 |
| 183 and 111 | 6771 |
| 169 and 170 | 28730 |
| 189 and 199 | 37611 |
| 165 and 51 | 2805 |