Least Common Multiple (LCM) of 110 and 198
The least common multiple (LCM) of 110 and 198 is 990.
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 110 and 198?
First, calculate the GCD of 110 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 198 = 0 remainder 110 |
| 2 | 198 ÷ 110 = 1 remainder 88 |
| 3 | 110 ÷ 88 = 1 remainder 22 |
| 4 | 88 ÷ 22 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 70 | 4690 |
| 162 and 189 | 1134 |
| 200 and 58 | 5800 |
| 106 and 192 | 10176 |
| 146 and 44 | 3212 |