Least Common Multiple (LCM) of 100 and 198
The least common multiple (LCM) of 100 and 198 is 9900.
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 100 and 198?
First, calculate the GCD of 100 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 198 = 0 remainder 100 |
| 2 | 198 ÷ 100 = 1 remainder 98 |
| 3 | 100 ÷ 98 = 1 remainder 2 |
| 4 | 98 ÷ 2 = 49 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 71 | 994 |
| 57 and 117 | 2223 |
| 81 and 16 | 1296 |
| 135 and 46 | 6210 |
| 63 and 70 | 630 |