Least Common Multiple (LCM) of 175 and 198
The least common multiple (LCM) of 175 and 198 is 34650.
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 198?
First, calculate the GCD of 175 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 198 = 0 remainder 175 |
| 2 | 198 ÷ 175 = 1 remainder 23 |
| 3 | 175 ÷ 23 = 7 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 83 | 4814 |
| 107 and 116 | 12412 |
| 106 and 71 | 7526 |
| 12 and 129 | 516 |
| 100 and 112 | 2800 |