Least Common Multiple (LCM) of 102 and 173
The least common multiple (LCM) of 102 and 173 is 17646.
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 102 and 173?
First, calculate the GCD of 102 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 173 = 0 remainder 102 |
| 2 | 173 ÷ 102 = 1 remainder 71 |
| 3 | 102 ÷ 71 = 1 remainder 31 |
| 4 | 71 ÷ 31 = 2 remainder 9 |
| 5 | 31 ÷ 9 = 3 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 108 | 540 |
| 22 and 62 | 682 |
| 37 and 134 | 4958 |
| 180 and 198 | 1980 |
| 106 and 46 | 2438 |