Least Common Multiple (LCM) of 144 and 163
The least common multiple (LCM) of 144 and 163 is 23472.
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 144 and 163?
First, calculate the GCD of 144 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 163 = 0 remainder 144 |
| 2 | 163 ÷ 144 = 1 remainder 19 |
| 3 | 144 ÷ 19 = 7 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 162 | 324 |
| 46 and 158 | 3634 |
| 34 and 113 | 3842 |
| 142 and 14 | 994 |
| 171 and 123 | 7011 |