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 |
|---|---|
| 100 and 195 | 3900 |
| 15 and 143 | 2145 |
| 167 and 40 | 6680 |
| 109 and 166 | 18094 |
| 190 and 54 | 5130 |