Least Common Multiple (LCM) of 107 and 171
The least common multiple (LCM) of 107 and 171 is 18297.
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 171?
First, calculate the GCD of 107 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 171 = 0 remainder 107 |
| 2 | 171 ÷ 107 = 1 remainder 64 |
| 3 | 107 ÷ 64 = 1 remainder 43 |
| 4 | 64 ÷ 43 = 1 remainder 21 |
| 5 | 43 ÷ 21 = 2 remainder 1 |
| 6 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 165 | 17490 |
| 42 and 162 | 1134 |
| 15 and 69 | 345 |
| 79 and 89 | 7031 |
| 149 and 119 | 17731 |