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 |
|---|---|
| 105 and 136 | 14280 |
| 119 and 22 | 2618 |
| 132 and 106 | 6996 |
| 170 and 200 | 3400 |
| 188 and 170 | 15980 |