Least Common Multiple (LCM) of 198 and 175
The least common multiple (LCM) of 198 and 175 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 198 and 175?
First, calculate the GCD of 198 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 175 = 1 remainder 23 |
| 2 | 175 ÷ 23 = 7 remainder 14 |
| 3 | 23 ÷ 14 = 1 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 112 | 224 |
| 97 and 72 | 6984 |
| 133 and 97 | 12901 |
| 38 and 161 | 6118 |
| 74 and 100 | 3700 |