Least Common Multiple (LCM) of 150 and 82
The least common multiple (LCM) of 150 and 82 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 150 and 82?
First, calculate the GCD of 150 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 82 = 1 remainder 68 |
| 2 | 82 ÷ 68 = 1 remainder 14 |
| 3 | 68 ÷ 14 = 4 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 115 | 8165 |
| 34 and 28 | 476 |
| 135 and 57 | 2565 |
| 97 and 27 | 2619 |
| 160 and 63 | 10080 |