Least Common Multiple (LCM) of 183 and 106
The least common multiple (LCM) of 183 and 106 is 19398.
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 183 and 106?
First, calculate the GCD of 183 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 183 ÷ 106 = 1 remainder 77 |
| 2 | 106 ÷ 77 = 1 remainder 29 |
| 3 | 77 ÷ 29 = 2 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 68 | 7140 |
| 175 and 103 | 18025 |
| 44 and 75 | 3300 |
| 16 and 123 | 1968 |
| 36 and 55 | 1980 |