Least Common Multiple (LCM) of 113 and 159
The least common multiple (LCM) of 113 and 159 is 17967.
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 113 and 159?
First, calculate the GCD of 113 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 159 = 0 remainder 113 |
| 2 | 159 ÷ 113 = 1 remainder 46 |
| 3 | 113 ÷ 46 = 2 remainder 21 |
| 4 | 46 ÷ 21 = 2 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 101 | 9595 |
| 195 and 11 | 2145 |
| 96 and 180 | 1440 |
| 119 and 120 | 14280 |
| 65 and 166 | 10790 |