Least Common Multiple (LCM) of 113 and 198
The least common multiple (LCM) of 113 and 198 is 22374.
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 113 and 198?
First, calculate the GCD of 113 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 198 = 0 remainder 113 |
| 2 | 198 ÷ 113 = 1 remainder 85 |
| 3 | 113 ÷ 85 = 1 remainder 28 |
| 4 | 85 ÷ 28 = 3 remainder 1 |
| 5 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 99 | 990 |
| 140 and 163 | 22820 |
| 78 and 92 | 3588 |
| 90 and 61 | 5490 |
| 180 and 71 | 12780 |