Least Common Multiple (LCM) of 144 and 177
The least common multiple (LCM) of 144 and 177 is 8496.
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 177?
First, calculate the GCD of 144 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 177 = 0 remainder 144 |
| 2 | 177 ÷ 144 = 1 remainder 33 |
| 3 | 144 ÷ 33 = 4 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 16 | 1552 |
| 147 and 190 | 27930 |
| 37 and 63 | 2331 |
| 68 and 24 | 408 |
| 105 and 168 | 840 |