Least Common Multiple (LCM) of 107 and 163
The least common multiple (LCM) of 107 and 163 is 17441.
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 163?
First, calculate the GCD of 107 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 163 = 0 remainder 107 |
| 2 | 163 ÷ 107 = 1 remainder 56 |
| 3 | 107 ÷ 56 = 1 remainder 51 |
| 4 | 56 ÷ 51 = 1 remainder 5 |
| 5 | 51 ÷ 5 = 10 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 159 | 7155 |
| 31 and 189 | 5859 |
| 76 and 109 | 8284 |
| 87 and 136 | 11832 |
| 117 and 123 | 4797 |