Least Common Multiple (LCM) of 71 and 192
The least common multiple (LCM) of 71 and 192 is 13632.
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 71 and 192?
First, calculate the GCD of 71 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 192 = 0 remainder 71 |
| 2 | 192 ÷ 71 = 2 remainder 50 |
| 3 | 71 ÷ 50 = 1 remainder 21 |
| 4 | 50 ÷ 21 = 2 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 98 | 6566 |
| 175 and 128 | 22400 |
| 169 and 185 | 31265 |
| 43 and 59 | 2537 |
| 172 and 117 | 20124 |