Least Common Multiple (LCM) of 75 and 193
The least common multiple (LCM) of 75 and 193 is 14475.
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 193?
First, calculate the GCD of 75 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 193 = 0 remainder 75 |
| 2 | 193 ÷ 75 = 2 remainder 43 |
| 3 | 75 ÷ 43 = 1 remainder 32 |
| 4 | 43 ÷ 32 = 1 remainder 11 |
| 5 | 32 ÷ 11 = 2 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 145 | 26970 |
| 103 and 95 | 9785 |
| 39 and 36 | 468 |
| 123 and 40 | 4920 |
| 167 and 25 | 4175 |