Least Common Multiple (LCM) of 77 and 82
The least common multiple (LCM) of 77 and 82 is 6314.
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 77 and 82?
First, calculate the GCD of 77 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 82 = 0 remainder 77 |
| 2 | 82 ÷ 77 = 1 remainder 5 |
| 3 | 77 ÷ 5 = 15 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 196 | 8428 |
| 104 and 139 | 14456 |
| 100 and 32 | 800 |
| 24 and 156 | 312 |
| 174 and 58 | 174 |