Least Common Multiple (LCM) of 198 and 56
The least common multiple (LCM) of 198 and 56 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 198 and 56?
First, calculate the GCD of 198 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 56 = 3 remainder 30 |
| 2 | 56 ÷ 30 = 1 remainder 26 |
| 3 | 30 ÷ 26 = 1 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 162 | 8910 |
| 107 and 127 | 13589 |
| 185 and 122 | 22570 |
| 180 and 80 | 720 |
| 196 and 87 | 17052 |