Least Common Multiple (LCM) of 52 and 198
The least common multiple (LCM) of 52 and 198 is 5148.
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 52 and 198?
First, calculate the GCD of 52 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 198 = 0 remainder 52 |
| 2 | 198 ÷ 52 = 3 remainder 42 |
| 3 | 52 ÷ 42 = 1 remainder 10 |
| 4 | 42 ÷ 10 = 4 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 11 | 1276 |
| 124 and 112 | 3472 |
| 56 and 77 | 616 |
| 124 and 107 | 13268 |
| 20 and 72 | 360 |