Least Common Multiple (LCM) of 110 and 144
The least common multiple (LCM) of 110 and 144 is 7920.
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 110 and 144?
First, calculate the GCD of 110 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 144 = 0 remainder 110 |
| 2 | 144 ÷ 110 = 1 remainder 34 |
| 3 | 110 ÷ 34 = 3 remainder 8 |
| 4 | 34 ÷ 8 = 4 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 40 | 1080 |
| 128 and 84 | 2688 |
| 47 and 178 | 8366 |
| 32 and 68 | 544 |
| 144 and 183 | 8784 |