Least Common Multiple (LCM) of 55 and 191
The least common multiple (LCM) of 55 and 191 is 10505.
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 191?
First, calculate the GCD of 55 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 191 = 0 remainder 55 |
| 2 | 191 ÷ 55 = 3 remainder 26 |
| 3 | 55 ÷ 26 = 2 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 119 | 14280 |
| 54 and 103 | 5562 |
| 130 and 122 | 7930 |
| 168 and 78 | 2184 |
| 197 and 51 | 10047 |