Least Common Multiple (LCM) of 105 and 182
The least common multiple (LCM) of 105 and 182 is 2730.
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 182?
First, calculate the GCD of 105 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 182 = 0 remainder 105 |
| 2 | 182 ÷ 105 = 1 remainder 77 |
| 3 | 105 ÷ 77 = 1 remainder 28 |
| 4 | 77 ÷ 28 = 2 remainder 21 |
| 5 | 28 ÷ 21 = 1 remainder 7 |
| 6 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 158 | 25122 |
| 200 and 137 | 27400 |
| 179 and 16 | 2864 |
| 31 and 149 | 4619 |
| 198 and 69 | 4554 |