Least Common Multiple (LCM) of 197 and 110
The least common multiple (LCM) of 197 and 110 is 21670.
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 110?
First, calculate the GCD of 197 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 110 = 1 remainder 87 |
| 2 | 110 ÷ 87 = 1 remainder 23 |
| 3 | 87 ÷ 23 = 3 remainder 18 |
| 4 | 23 ÷ 18 = 1 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 129 | 12642 |
| 105 and 187 | 19635 |
| 168 and 172 | 7224 |
| 82 and 184 | 7544 |
| 147 and 165 | 8085 |