Least Common Multiple (LCM) of 126 and 198
The least common multiple (LCM) of 126 and 198 is 1386.
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 126 and 198?
First, calculate the GCD of 126 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 198 = 0 remainder 126 |
| 2 | 198 ÷ 126 = 1 remainder 72 |
| 3 | 126 ÷ 72 = 1 remainder 54 |
| 4 | 72 ÷ 54 = 1 remainder 18 |
| 5 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 83 | 913 |
| 43 and 129 | 129 |
| 115 and 132 | 15180 |
| 64 and 125 | 8000 |
| 11 and 102 | 1122 |