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 |
|---|---|
| 162 and 140 | 11340 |
| 160 and 60 | 480 |
| 86 and 101 | 8686 |
| 116 and 55 | 6380 |
| 110 and 80 | 880 |