Least Common Multiple (LCM) of 67 and 163
The least common multiple (LCM) of 67 and 163 is 10921.
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 163?
First, calculate the GCD of 67 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 163 = 0 remainder 67 |
| 2 | 163 ÷ 67 = 2 remainder 29 |
| 3 | 67 ÷ 29 = 2 remainder 9 |
| 4 | 29 ÷ 9 = 3 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 57 | 285 |
| 47 and 78 | 3666 |
| 88 and 152 | 1672 |
| 90 and 89 | 8010 |
| 56 and 35 | 280 |