Least Common Multiple (LCM) of 16 and 198
The least common multiple (LCM) of 16 and 198 is 1584.
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 16 and 198?
First, calculate the GCD of 16 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 198 = 0 remainder 16 |
| 2 | 198 ÷ 16 = 12 remainder 6 |
| 3 | 16 ÷ 6 = 2 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 165 | 4785 |
| 36 and 138 | 828 |
| 152 and 196 | 7448 |
| 116 and 21 | 2436 |
| 164 and 143 | 23452 |