Least Common Multiple (LCM) of 106 and 65
The least common multiple (LCM) of 106 and 65 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 106 and 65?
First, calculate the GCD of 106 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 65 = 1 remainder 41 |
| 2 | 65 ÷ 41 = 1 remainder 24 |
| 3 | 41 ÷ 24 = 1 remainder 17 |
| 4 | 24 ÷ 17 = 1 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 15 | 2280 |
| 193 and 109 | 21037 |
| 159 and 102 | 5406 |
| 134 and 126 | 8442 |
| 151 and 55 | 8305 |