Least Common Multiple (LCM) of 163 and 103
The least common multiple (LCM) of 163 and 103 is 16789.
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 163 and 103?
First, calculate the GCD of 163 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 103 = 1 remainder 60 |
| 2 | 103 ÷ 60 = 1 remainder 43 |
| 3 | 60 ÷ 43 = 1 remainder 17 |
| 4 | 43 ÷ 17 = 2 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 63 | 1638 |
| 120 and 162 | 3240 |
| 24 and 85 | 2040 |
| 134 and 147 | 19698 |
| 82 and 32 | 1312 |