Least Common Multiple (LCM) of 56 and 198
The least common multiple (LCM) of 56 and 198 is 5544.
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 56 and 198?
First, calculate the GCD of 56 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 198 = 0 remainder 56 |
| 2 | 198 ÷ 56 = 3 remainder 30 |
| 3 | 56 ÷ 30 = 1 remainder 26 |
| 4 | 30 ÷ 26 = 1 remainder 4 |
| 5 | 26 ÷ 4 = 6 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 182 | 2002 |
| 166 and 118 | 9794 |
| 135 and 157 | 21195 |
| 162 and 89 | 14418 |
| 57 and 189 | 3591 |