Least Common Multiple (LCM) of 159 and 112
The least common multiple (LCM) of 159 and 112 is 17808.
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 112?
First, calculate the GCD of 159 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 112 = 1 remainder 47 |
| 2 | 112 ÷ 47 = 2 remainder 18 |
| 3 | 47 ÷ 18 = 2 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 27 | 1242 |
| 42 and 16 | 336 |
| 177 and 21 | 1239 |
| 99 and 182 | 18018 |
| 25 and 110 | 550 |