Least Common Multiple (LCM) of 144 and 171
The least common multiple (LCM) of 144 and 171 is 2736.
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 171?
First, calculate the GCD of 144 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 171 = 0 remainder 144 |
| 2 | 171 ÷ 144 = 1 remainder 27 |
| 3 | 144 ÷ 27 = 5 remainder 9 |
| 4 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 29 | 1943 |
| 74 and 28 | 1036 |
| 173 and 105 | 18165 |
| 16 and 83 | 1328 |
| 47 and 83 | 3901 |