Least Common Multiple (LCM) of 107 and 165
The least common multiple (LCM) of 107 and 165 is 17655.
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 165?
First, calculate the GCD of 107 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 165 = 0 remainder 107 |
| 2 | 165 ÷ 107 = 1 remainder 58 |
| 3 | 107 ÷ 58 = 1 remainder 49 |
| 4 | 58 ÷ 49 = 1 remainder 9 |
| 5 | 49 ÷ 9 = 5 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 25 | 4525 |
| 122 and 131 | 15982 |
| 18 and 41 | 738 |
| 110 and 128 | 7040 |
| 12 and 70 | 420 |