Least Common Multiple (LCM) of 163 and 48
The least common multiple (LCM) of 163 and 48 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 163 and 48?
First, calculate the GCD of 163 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 48 = 3 remainder 19 |
| 2 | 48 ÷ 19 = 2 remainder 10 |
| 3 | 19 ÷ 10 = 1 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 69 | 7521 |
| 32 and 161 | 5152 |
| 184 and 167 | 30728 |
| 188 and 179 | 33652 |
| 178 and 178 | 178 |