Least Common Multiple (LCM) of 105 and 181
The least common multiple (LCM) of 105 and 181 is 19005.
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 181?
First, calculate the GCD of 105 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 181 = 0 remainder 105 |
| 2 | 181 ÷ 105 = 1 remainder 76 |
| 3 | 105 ÷ 76 = 1 remainder 29 |
| 4 | 76 ÷ 29 = 2 remainder 18 |
| 5 | 29 ÷ 18 = 1 remainder 11 |
| 6 | 18 ÷ 11 = 1 remainder 7 |
| 7 | 11 ÷ 7 = 1 remainder 4 |
| 8 | 7 ÷ 4 = 1 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 113 | 5650 |
| 96 and 51 | 1632 |
| 42 and 137 | 5754 |
| 106 and 117 | 12402 |
| 129 and 195 | 8385 |