Least Common Multiple (LCM) of 43 and 163
The least common multiple (LCM) of 43 and 163 is 7009.
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 43 and 163?
First, calculate the GCD of 43 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 163 = 0 remainder 43 |
| 2 | 163 ÷ 43 = 3 remainder 34 |
| 3 | 43 ÷ 34 = 1 remainder 9 |
| 4 | 34 ÷ 9 = 3 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 21 | 1302 |
| 123 and 74 | 9102 |
| 147 and 101 | 14847 |
| 143 and 137 | 19591 |
| 160 and 78 | 6240 |