Least Common Multiple (LCM) of 143 and 103
The least common multiple (LCM) of 143 and 103 is 14729.
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 143 and 103?
First, calculate the GCD of 143 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 103 = 1 remainder 40 |
| 2 | 103 ÷ 40 = 2 remainder 23 |
| 3 | 40 ÷ 23 = 1 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 25 | 350 |
| 35 and 104 | 3640 |
| 27 and 30 | 270 |
| 180 and 142 | 12780 |
| 176 and 111 | 19536 |