Least Common Multiple (LCM) of 185 and 106
The least common multiple (LCM) of 185 and 106 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 185 and 106?
First, calculate the GCD of 185 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 106 = 1 remainder 79 |
| 2 | 106 ÷ 79 = 1 remainder 27 |
| 3 | 79 ÷ 27 = 2 remainder 25 |
| 4 | 27 ÷ 25 = 1 remainder 2 |
| 5 | 25 ÷ 2 = 12 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 120 | 12840 |
| 79 and 156 | 12324 |
| 165 and 109 | 17985 |
| 23 and 194 | 4462 |
| 56 and 39 | 2184 |