Least Common Multiple (LCM) of 82 and 150
The least common multiple (LCM) of 82 and 150 is 6150.
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 150?
First, calculate the GCD of 82 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 150 = 0 remainder 82 |
| 2 | 150 ÷ 82 = 1 remainder 68 |
| 3 | 82 ÷ 68 = 1 remainder 14 |
| 4 | 68 ÷ 14 = 4 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 36 | 684 |
| 140 and 21 | 420 |
| 75 and 29 | 2175 |
| 101 and 41 | 4141 |
| 164 and 67 | 10988 |