Least Common Multiple (LCM) of 55 and 198
The least common multiple (LCM) of 55 and 198 is 990.
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 55 and 198?
First, calculate the GCD of 55 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 198 = 0 remainder 55 |
| 2 | 198 ÷ 55 = 3 remainder 33 |
| 3 | 55 ÷ 33 = 1 remainder 22 |
| 4 | 33 ÷ 22 = 1 remainder 11 |
| 5 | 22 ÷ 11 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 26 | 858 |
| 135 and 148 | 19980 |
| 119 and 186 | 22134 |
| 179 and 23 | 4117 |
| 109 and 77 | 8393 |