Least Common Multiple (LCM) of 198 and 113
The least common multiple (LCM) of 198 and 113 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 198 and 113?
First, calculate the GCD of 198 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 113 = 1 remainder 85 |
| 2 | 113 ÷ 85 = 1 remainder 28 |
| 3 | 85 ÷ 28 = 3 remainder 1 |
| 4 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 46 | 1334 |
| 37 and 178 | 6586 |
| 26 and 105 | 2730 |
| 102 and 102 | 102 |
| 182 and 119 | 3094 |