Least Common Multiple (LCM) of 198 and 105
The least common multiple (LCM) of 198 and 105 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 198 and 105?
First, calculate the GCD of 198 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 105 = 1 remainder 93 |
| 2 | 105 ÷ 93 = 1 remainder 12 |
| 3 | 93 ÷ 12 = 7 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 78 | 1872 |
| 36 and 12 | 36 |
| 137 and 98 | 13426 |
| 137 and 172 | 23564 |
| 75 and 36 | 900 |