Least Common Multiple (LCM) of 105 and 198
The least common multiple (LCM) of 105 and 198 is 6930.
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 105 and 198?
First, calculate the GCD of 105 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 198 = 0 remainder 105 |
| 2 | 198 ÷ 105 = 1 remainder 93 |
| 3 | 105 ÷ 93 = 1 remainder 12 |
| 4 | 93 ÷ 12 = 7 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 110 | 1430 |
| 176 and 109 | 19184 |
| 128 and 150 | 9600 |
| 41 and 57 | 2337 |
| 50 and 54 | 1350 |