Least Common Multiple (LCM) of 112 and 159
The least common multiple (LCM) of 112 and 159 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 112 and 159?
First, calculate the GCD of 112 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 159 = 0 remainder 112 |
| 2 | 159 ÷ 112 = 1 remainder 47 |
| 3 | 112 ÷ 47 = 2 remainder 18 |
| 4 | 47 ÷ 18 = 2 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 93 | 17670 |
| 39 and 188 | 7332 |
| 84 and 105 | 420 |
| 131 and 89 | 11659 |
| 137 and 146 | 20002 |