Least Common Multiple (LCM) of 112 and 198
The least common multiple (LCM) of 112 and 198 is 11088.
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 112 and 198?
First, calculate the GCD of 112 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 198 = 0 remainder 112 |
| 2 | 198 ÷ 112 = 1 remainder 86 |
| 3 | 112 ÷ 86 = 1 remainder 26 |
| 4 | 86 ÷ 26 = 3 remainder 8 |
| 5 | 26 ÷ 8 = 3 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 55 | 2035 |
| 90 and 135 | 270 |
| 123 and 99 | 4059 |
| 95 and 155 | 2945 |
| 138 and 69 | 138 |