Least Common Multiple (LCM) of 104 and 144
The least common multiple (LCM) of 104 and 144 is 1872.
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 104 and 144?
First, calculate the GCD of 104 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 144 = 0 remainder 104 |
| 2 | 144 ÷ 104 = 1 remainder 40 |
| 3 | 104 ÷ 40 = 2 remainder 24 |
| 4 | 40 ÷ 24 = 1 remainder 16 |
| 5 | 24 ÷ 16 = 1 remainder 8 |
| 6 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 104 | 1040 |
| 199 and 111 | 22089 |
| 137 and 61 | 8357 |
| 96 and 77 | 7392 |
| 158 and 154 | 12166 |