Least Common Multiple (LCM) of 103 and 159
The least common multiple (LCM) of 103 and 159 is 16377.
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 159?
First, calculate the GCD of 103 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 159 = 0 remainder 103 |
| 2 | 159 ÷ 103 = 1 remainder 56 |
| 3 | 103 ÷ 56 = 1 remainder 47 |
| 4 | 56 ÷ 47 = 1 remainder 9 |
| 5 | 47 ÷ 9 = 5 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 191 | 21774 |
| 37 and 34 | 1258 |
| 109 and 53 | 5777 |
| 89 and 104 | 9256 |
| 45 and 199 | 8955 |