Least Common Multiple (LCM) of 173 and 105
The least common multiple (LCM) of 173 and 105 is 18165.
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 105?
First, calculate the GCD of 173 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 105 = 1 remainder 68 |
| 2 | 105 ÷ 68 = 1 remainder 37 |
| 3 | 68 ÷ 37 = 1 remainder 31 |
| 4 | 37 ÷ 31 = 1 remainder 6 |
| 5 | 31 ÷ 6 = 5 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 106 | 7632 |
| 122 and 97 | 11834 |
| 40 and 58 | 1160 |
| 184 and 80 | 1840 |
| 111 and 78 | 2886 |