Least Common Multiple (LCM) of 48 and 163
The least common multiple (LCM) of 48 and 163 is 7824.
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 48 and 163?
First, calculate the GCD of 48 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 163 = 0 remainder 48 |
| 2 | 163 ÷ 48 = 3 remainder 19 |
| 3 | 48 ÷ 19 = 2 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 175 | 34475 |
| 105 and 58 | 6090 |
| 70 and 11 | 770 |
| 142 and 172 | 12212 |
| 180 and 190 | 3420 |