Least Common Multiple (LCM) of 107 and 173
The least common multiple (LCM) of 107 and 173 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 107 and 173?
First, calculate the GCD of 107 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 173 = 0 remainder 107 |
| 2 | 173 ÷ 107 = 1 remainder 66 |
| 3 | 107 ÷ 66 = 1 remainder 41 |
| 4 | 66 ÷ 41 = 1 remainder 25 |
| 5 | 41 ÷ 25 = 1 remainder 16 |
| 6 | 25 ÷ 16 = 1 remainder 9 |
| 7 | 16 ÷ 9 = 1 remainder 7 |
| 8 | 9 ÷ 7 = 1 remainder 2 |
| 9 | 7 ÷ 2 = 3 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 55 | 495 |
| 118 and 188 | 11092 |
| 172 and 49 | 8428 |
| 120 and 87 | 3480 |
| 80 and 115 | 1840 |