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 |
|---|---|
| 180 and 197 | 35460 |
| 84 and 132 | 924 |
| 44 and 149 | 6556 |
| 124 and 78 | 4836 |
| 199 and 55 | 10945 |