Least Common Multiple (LCM) of 144 and 178
The least common multiple (LCM) of 144 and 178 is 12816.
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 178?
First, calculate the GCD of 144 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 178 = 0 remainder 144 |
| 2 | 178 ÷ 144 = 1 remainder 34 |
| 3 | 144 ÷ 34 = 4 remainder 8 |
| 4 | 34 ÷ 8 = 4 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 33 | 3597 |
| 49 and 164 | 8036 |
| 51 and 90 | 1530 |
| 60 and 163 | 9780 |
| 146 and 118 | 8614 |