Least Common Multiple (LCM) of 114 and 198
The least common multiple (LCM) of 114 and 198 is 3762.
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 114 and 198?
First, calculate the GCD of 114 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 198 = 0 remainder 114 |
| 2 | 198 ÷ 114 = 1 remainder 84 |
| 3 | 114 ÷ 84 = 1 remainder 30 |
| 4 | 84 ÷ 30 = 2 remainder 24 |
| 5 | 30 ÷ 24 = 1 remainder 6 |
| 6 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 113 | 11526 |
| 125 and 65 | 1625 |
| 118 and 81 | 9558 |
| 144 and 73 | 10512 |
| 17 and 122 | 2074 |