Least Common Multiple (LCM) of 198 and 29
The least common multiple (LCM) of 198 and 29 is 5742.
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 29?
First, calculate the GCD of 198 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 29 = 6 remainder 24 |
| 2 | 29 ÷ 24 = 1 remainder 5 |
| 3 | 24 ÷ 5 = 4 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 107 | 4387 |
| 34 and 179 | 6086 |
| 78 and 159 | 4134 |
| 102 and 200 | 10200 |
| 75 and 122 | 9150 |