Least Common Multiple (LCM) of 30 and 82
The least common multiple (LCM) of 30 and 82 is 1230.
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 30 and 82?
First, calculate the GCD of 30 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 82 = 0 remainder 30 |
| 2 | 82 ÷ 30 = 2 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 136 | 13464 |
| 118 and 50 | 2950 |
| 130 and 178 | 11570 |
| 132 and 49 | 6468 |
| 182 and 55 | 10010 |