Least Common Multiple (LCM) of 82 and 176
The least common multiple (LCM) of 82 and 176 is 7216.
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 82 and 176?
First, calculate the GCD of 82 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 176 = 0 remainder 82 |
| 2 | 176 ÷ 82 = 2 remainder 12 |
| 3 | 82 ÷ 12 = 6 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 41 | 3567 |
| 161 and 123 | 19803 |
| 108 and 126 | 756 |
| 198 and 92 | 9108 |
| 10 and 89 | 890 |