Least Common Multiple (LCM) of 52 and 193
The least common multiple (LCM) of 52 and 193 is 10036.
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 193?
First, calculate the GCD of 52 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 193 = 0 remainder 52 |
| 2 | 193 ÷ 52 = 3 remainder 37 |
| 3 | 52 ÷ 37 = 1 remainder 15 |
| 4 | 37 ÷ 15 = 2 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 110 | 330 |
| 159 and 41 | 6519 |
| 197 and 187 | 36839 |
| 128 and 20 | 640 |
| 198 and 77 | 1386 |