Least Common Multiple (LCM) of 175 and 193
The least common multiple (LCM) of 175 and 193 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 175 and 193?
First, calculate the GCD of 175 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 193 = 0 remainder 175 |
| 2 | 193 ÷ 175 = 1 remainder 18 |
| 3 | 175 ÷ 18 = 9 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 36 | 828 |
| 113 and 144 | 16272 |
| 71 and 102 | 7242 |
| 174 and 100 | 8700 |
| 38 and 25 | 950 |