Least Common Multiple (LCM) of 193 and 175
The least common multiple (LCM) of 193 and 175 is 33775.
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 193 and 175?
First, calculate the GCD of 193 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 175 = 1 remainder 18 |
| 2 | 175 ÷ 18 = 9 remainder 13 |
| 3 | 18 ÷ 13 = 1 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 11 | 506 |
| 85 and 25 | 425 |
| 29 and 18 | 522 |
| 141 and 139 | 19599 |
| 168 and 17 | 2856 |