Least Common Multiple (LCM) of 144 and 103
The least common multiple (LCM) of 144 and 103 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 144 and 103?
First, calculate the GCD of 144 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 103 = 1 remainder 41 |
| 2 | 103 ÷ 41 = 2 remainder 21 |
| 3 | 41 ÷ 21 = 1 remainder 20 |
| 4 | 21 ÷ 20 = 1 remainder 1 |
| 5 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 61 | 7808 |
| 51 and 182 | 9282 |
| 102 and 127 | 12954 |
| 64 and 75 | 4800 |
| 40 and 20 | 40 |