Least Common Multiple (LCM) of 103 and 144
The least common multiple (LCM) of 103 and 144 is 14832.
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 103 and 144?
First, calculate the GCD of 103 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 144 = 0 remainder 103 |
| 2 | 144 ÷ 103 = 1 remainder 41 |
| 3 | 103 ÷ 41 = 2 remainder 21 |
| 4 | 41 ÷ 21 = 1 remainder 20 |
| 5 | 21 ÷ 20 = 1 remainder 1 |
| 6 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 169 | 14027 |
| 113 and 39 | 4407 |
| 68 and 74 | 2516 |
| 98 and 78 | 3822 |
| 185 and 144 | 26640 |