Least Common Multiple (LCM) of 103 and 143
The least common multiple (LCM) of 103 and 143 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 103 and 143?
First, calculate the GCD of 103 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 143 = 0 remainder 103 |
| 2 | 143 ÷ 103 = 1 remainder 40 |
| 3 | 103 ÷ 40 = 2 remainder 23 |
| 4 | 40 ÷ 23 = 1 remainder 17 |
| 5 | 23 ÷ 17 = 1 remainder 6 |
| 6 | 17 ÷ 6 = 2 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 31 | 3782 |
| 117 and 55 | 6435 |
| 31 and 78 | 2418 |
| 31 and 50 | 1550 |
| 104 and 155 | 16120 |