Least Common Multiple (LCM) of 21 and 163
The least common multiple (LCM) of 21 and 163 is 3423.
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 21 and 163?
First, calculate the GCD of 21 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 163 = 0 remainder 21 |
| 2 | 163 ÷ 21 = 7 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 193 | 34740 |
| 106 and 89 | 9434 |
| 191 and 127 | 24257 |
| 151 and 175 | 26425 |
| 74 and 149 | 11026 |