Least Common Multiple (LCM) of 175 and 195
The least common multiple (LCM) of 175 and 195 is 6825.
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 195?
First, calculate the GCD of 175 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 195 = 0 remainder 175 |
| 2 | 195 ÷ 175 = 1 remainder 20 |
| 3 | 175 ÷ 20 = 8 remainder 15 |
| 4 | 20 ÷ 15 = 1 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 123 | 7872 |
| 129 and 75 | 3225 |
| 32 and 181 | 5792 |
| 196 and 98 | 196 |
| 53 and 65 | 3445 |