Least Common Multiple (LCM) of 191 and 105
The least common multiple (LCM) of 191 and 105 is 20055.
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 191 and 105?
First, calculate the GCD of 191 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 105 = 1 remainder 86 |
| 2 | 105 ÷ 86 = 1 remainder 19 |
| 3 | 86 ÷ 19 = 4 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 109 | 18312 |
| 87 and 124 | 10788 |
| 178 and 31 | 5518 |
| 22 and 30 | 330 |
| 55 and 20 | 220 |