Least Common Multiple (LCM) of 106 and 173
The least common multiple (LCM) of 106 and 173 is 18338.
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 173?
First, calculate the GCD of 106 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 173 = 0 remainder 106 |
| 2 | 173 ÷ 106 = 1 remainder 67 |
| 3 | 106 ÷ 67 = 1 remainder 39 |
| 4 | 67 ÷ 39 = 1 remainder 28 |
| 5 | 39 ÷ 28 = 1 remainder 11 |
| 6 | 28 ÷ 11 = 2 remainder 6 |
| 7 | 11 ÷ 6 = 1 remainder 5 |
| 8 | 6 ÷ 5 = 1 remainder 1 |
| 9 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 193 | 36477 |
| 92 and 109 | 10028 |
| 100 and 51 | 5100 |
| 162 and 149 | 24138 |
| 159 and 54 | 2862 |