Least Common Multiple (LCM) of 106 and 185
The least common multiple (LCM) of 106 and 185 is 19610.
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 185?
First, calculate the GCD of 106 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 185 = 0 remainder 106 |
| 2 | 185 ÷ 106 = 1 remainder 79 |
| 3 | 106 ÷ 79 = 1 remainder 27 |
| 4 | 79 ÷ 27 = 2 remainder 25 |
| 5 | 27 ÷ 25 = 1 remainder 2 |
| 6 | 25 ÷ 2 = 12 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 28 | 4844 |
| 114 and 36 | 684 |
| 198 and 122 | 12078 |
| 67 and 191 | 12797 |
| 42 and 54 | 378 |