Least Common Multiple (LCM) of 159 and 103
The least common multiple (LCM) of 159 and 103 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 159 and 103?
First, calculate the GCD of 159 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 103 = 1 remainder 56 |
| 2 | 103 ÷ 56 = 1 remainder 47 |
| 3 | 56 ÷ 47 = 1 remainder 9 |
| 4 | 47 ÷ 9 = 5 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 63 | 7245 |
| 159 and 15 | 795 |
| 196 and 190 | 18620 |
| 168 and 149 | 25032 |
| 33 and 36 | 396 |