Least Common Multiple (LCM) of 65 and 192
The least common multiple (LCM) of 65 and 192 is 12480.
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 65 and 192?
First, calculate the GCD of 65 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 192 = 0 remainder 65 |
| 2 | 192 ÷ 65 = 2 remainder 62 |
| 3 | 65 ÷ 62 = 1 remainder 3 |
| 4 | 62 ÷ 3 = 20 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 141 | 24675 |
| 32 and 53 | 1696 |
| 138 and 127 | 17526 |
| 43 and 147 | 6321 |
| 131 and 16 | 2096 |