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 |
|---|---|
| 196 and 78 | 7644 |
| 172 and 51 | 8772 |
| 135 and 83 | 11205 |
| 124 and 13 | 1612 |
| 17 and 126 | 2142 |