Least Common Multiple (LCM) of 67 and 566
The least common multiple (LCM) of 67 and 566 is 37922.
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 67 and 566?
First, calculate the GCD of 67 and 566 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 566 = 0 remainder 67 |
| 2 | 566 ÷ 67 = 8 remainder 30 |
| 3 | 67 ÷ 30 = 2 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 146 | 2336 |
| 80 and 54 | 2160 |
| 86 and 198 | 8514 |
| 27 and 116 | 3132 |
| 52 and 19 | 988 |