Least Common Multiple (LCM) of 176 and 105
The least common multiple (LCM) of 176 and 105 is 18480.
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 176 and 105?
First, calculate the GCD of 176 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 105 = 1 remainder 71 |
| 2 | 105 ÷ 71 = 1 remainder 34 |
| 3 | 71 ÷ 34 = 2 remainder 3 |
| 4 | 34 ÷ 3 = 11 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 33 | 2145 |
| 147 and 58 | 8526 |
| 20 and 165 | 660 |
| 21 and 80 | 1680 |
| 158 and 198 | 15642 |