Least Common Multiple (LCM) of 65 and 106
The least common multiple (LCM) of 65 and 106 is 6890.
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 106?
First, calculate the GCD of 65 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 106 = 0 remainder 65 |
| 2 | 106 ÷ 65 = 1 remainder 41 |
| 3 | 65 ÷ 41 = 1 remainder 24 |
| 4 | 41 ÷ 24 = 1 remainder 17 |
| 5 | 24 ÷ 17 = 1 remainder 7 |
| 6 | 17 ÷ 7 = 2 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 119 | 2261 |
| 76 and 80 | 1520 |
| 57 and 181 | 10317 |
| 19 and 65 | 1235 |
| 112 and 199 | 22288 |