Least Common Multiple (LCM) of 75 and 43
The least common multiple (LCM) of 75 and 43 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 75 and 43?
First, calculate the GCD of 75 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 43 = 1 remainder 32 |
| 2 | 43 ÷ 32 = 1 remainder 11 |
| 3 | 32 ÷ 11 = 2 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 46 | 3266 |
| 15 and 118 | 1770 |
| 152 and 151 | 22952 |
| 92 and 18 | 828 |
| 84 and 121 | 10164 |