Least Common Multiple (LCM) of 82 and 111
The least common multiple (LCM) of 82 and 111 is 9102.
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 111?
First, calculate the GCD of 82 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 111 = 0 remainder 82 |
| 2 | 111 ÷ 82 = 1 remainder 29 |
| 3 | 82 ÷ 29 = 2 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 147 | 6321 |
| 98 and 195 | 19110 |
| 198 and 51 | 3366 |
| 105 and 169 | 17745 |
| 137 and 151 | 20687 |