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 |
|---|---|
| 81 and 36 | 324 |
| 138 and 30 | 690 |
| 172 and 132 | 5676 |
| 33 and 125 | 4125 |
| 105 and 192 | 6720 |