Least Common Multiple (LCM) of 175 and 197
The least common multiple (LCM) of 175 and 197 is 34475.
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 197?
First, calculate the GCD of 175 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 197 = 0 remainder 175 |
| 2 | 197 ÷ 175 = 1 remainder 22 |
| 3 | 175 ÷ 22 = 7 remainder 21 |
| 4 | 22 ÷ 21 = 1 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 102 | 102 |
| 90 and 194 | 8730 |
| 137 and 199 | 27263 |
| 148 and 183 | 27084 |
| 160 and 82 | 6560 |