Least Common Multiple (LCM) of 67 and 192
The least common multiple (LCM) of 67 and 192 is 12864.
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 192?
First, calculate the GCD of 67 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 192 = 0 remainder 67 |
| 2 | 192 ÷ 67 = 2 remainder 58 |
| 3 | 67 ÷ 58 = 1 remainder 9 |
| 4 | 58 ÷ 9 = 6 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 94 | 8366 |
| 94 and 136 | 6392 |
| 161 and 100 | 16100 |
| 105 and 165 | 1155 |
| 178 and 146 | 12994 |