Least Common Multiple (LCM) of 197 and 174
The least common multiple (LCM) of 197 and 174 is 34278.
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 197 and 174?
First, calculate the GCD of 197 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 174 = 1 remainder 23 |
| 2 | 174 ÷ 23 = 7 remainder 13 |
| 3 | 23 ÷ 13 = 1 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 159 | 5565 |
| 124 and 154 | 9548 |
| 65 and 106 | 6890 |
| 42 and 147 | 294 |
| 66 and 98 | 3234 |