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 |
|---|---|
| 138 and 114 | 2622 |
| 103 and 61 | 6283 |
| 114 and 156 | 2964 |
| 51 and 63 | 1071 |
| 20 and 122 | 1220 |