Least Common Multiple (LCM) of 34 and 197
The least common multiple (LCM) of 34 and 197 is 6698.
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 34 and 197?
First, calculate the GCD of 34 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 197 = 0 remainder 34 |
| 2 | 197 ÷ 34 = 5 remainder 27 |
| 3 | 34 ÷ 27 = 1 remainder 7 |
| 4 | 27 ÷ 7 = 3 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 28 | 3668 |
| 130 and 69 | 8970 |
| 147 and 133 | 2793 |
| 107 and 190 | 20330 |
| 109 and 124 | 13516 |