Least Common Multiple (LCM) of 55 and 193
The least common multiple (LCM) of 55 and 193 is 10615.
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 55 and 193?
First, calculate the GCD of 55 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 193 = 0 remainder 55 |
| 2 | 193 ÷ 55 = 3 remainder 28 |
| 3 | 55 ÷ 28 = 1 remainder 27 |
| 4 | 28 ÷ 27 = 1 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 67 | 7504 |
| 30 and 140 | 420 |
| 56 and 180 | 2520 |
| 176 and 73 | 12848 |
| 32 and 134 | 2144 |