Least Common Multiple (LCM) of 182 and 105
The least common multiple (LCM) of 182 and 105 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 182 and 105?
First, calculate the GCD of 182 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 182 ÷ 105 = 1 remainder 77 |
| 2 | 105 ÷ 77 = 1 remainder 28 |
| 3 | 77 ÷ 28 = 2 remainder 21 |
| 4 | 28 ÷ 21 = 1 remainder 7 |
| 5 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 67 | 12127 |
| 25 and 192 | 4800 |
| 162 and 177 | 9558 |
| 167 and 116 | 19372 |
| 112 and 185 | 20720 |