Least Common Multiple (LCM) of 144 and 104
The least common multiple (LCM) of 144 and 104 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 144 and 104?
First, calculate the GCD of 144 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 104 = 1 remainder 40 |
| 2 | 104 ÷ 40 = 2 remainder 24 |
| 3 | 40 ÷ 24 = 1 remainder 16 |
| 4 | 24 ÷ 16 = 1 remainder 8 |
| 5 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 138 | 3864 |
| 15 and 147 | 735 |
| 144 and 128 | 1152 |
| 34 and 137 | 4658 |
| 76 and 83 | 6308 |