Least Common Multiple (LCM) of 82 and 178
The least common multiple (LCM) of 82 and 178 is 7298.
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 178?
First, calculate the GCD of 82 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 178 = 0 remainder 82 |
| 2 | 178 ÷ 82 = 2 remainder 14 |
| 3 | 82 ÷ 14 = 5 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 168 | 2856 |
| 163 and 10 | 1630 |
| 145 and 199 | 28855 |
| 200 and 117 | 23400 |
| 54 and 10 | 270 |