Least Common Multiple (LCM) of 173 and 106
The least common multiple (LCM) of 173 and 106 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 173 and 106?
First, calculate the GCD of 173 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 106 = 1 remainder 67 |
| 2 | 106 ÷ 67 = 1 remainder 39 |
| 3 | 67 ÷ 39 = 1 remainder 28 |
| 4 | 39 ÷ 28 = 1 remainder 11 |
| 5 | 28 ÷ 11 = 2 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 56 | 560 |
| 166 and 13 | 2158 |
| 163 and 101 | 16463 |
| 23 and 78 | 1794 |
| 60 and 158 | 4740 |