Least Common Multiple (LCM) of 173 and 102
The least common multiple (LCM) of 173 and 102 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 173 and 102?
First, calculate the GCD of 173 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 102 = 1 remainder 71 |
| 2 | 102 ÷ 71 = 1 remainder 31 |
| 3 | 71 ÷ 31 = 2 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 20 | 260 |
| 195 and 20 | 780 |
| 106 and 106 | 106 |
| 166 and 97 | 16102 |
| 106 and 106 | 106 |