Least Common Multiple (LCM) of 105 and 191
The least common multiple (LCM) of 105 and 191 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 105 and 191?
First, calculate the GCD of 105 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 191 = 0 remainder 105 |
| 2 | 191 ÷ 105 = 1 remainder 86 |
| 3 | 105 ÷ 86 = 1 remainder 19 |
| 4 | 86 ÷ 19 = 4 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 18 | 1494 |
| 77 and 80 | 6160 |
| 160 and 137 | 21920 |
| 150 and 71 | 10650 |
| 121 and 144 | 17424 |