Least Common Multiple (LCM) of 173 and 107
The least common multiple (LCM) of 173 and 107 is 18511.
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 107?
First, calculate the GCD of 173 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 107 = 1 remainder 66 |
| 2 | 107 ÷ 66 = 1 remainder 41 |
| 3 | 66 ÷ 41 = 1 remainder 25 |
| 4 | 41 ÷ 25 = 1 remainder 16 |
| 5 | 25 ÷ 16 = 1 remainder 9 |
| 6 | 16 ÷ 9 = 1 remainder 7 |
| 7 | 9 ÷ 7 = 1 remainder 2 |
| 8 | 7 ÷ 2 = 3 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 185 | 5920 |
| 122 and 163 | 19886 |
| 114 and 66 | 1254 |
| 102 and 13 | 1326 |
| 83 and 87 | 7221 |