Least Common Multiple (LCM) of 197 and 114
The least common multiple (LCM) of 197 and 114 is 22458.
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 114?
First, calculate the GCD of 197 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 114 = 1 remainder 83 |
| 2 | 114 ÷ 83 = 1 remainder 31 |
| 3 | 83 ÷ 31 = 2 remainder 21 |
| 4 | 31 ÷ 21 = 1 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 192 | 12864 |
| 54 and 35 | 1890 |
| 199 and 68 | 13532 |
| 106 and 105 | 11130 |
| 131 and 162 | 21222 |