Least Common Multiple (LCM) of 115 and 159
The least common multiple (LCM) of 115 and 159 is 18285.
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 115 and 159?
First, calculate the GCD of 115 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 159 = 0 remainder 115 |
| 2 | 159 ÷ 115 = 1 remainder 44 |
| 3 | 115 ÷ 44 = 2 remainder 27 |
| 4 | 44 ÷ 27 = 1 remainder 17 |
| 5 | 27 ÷ 17 = 1 remainder 10 |
| 6 | 17 ÷ 10 = 1 remainder 7 |
| 7 | 10 ÷ 7 = 1 remainder 3 |
| 8 | 7 ÷ 3 = 2 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 109 | 11009 |
| 187 and 60 | 11220 |
| 42 and 113 | 4746 |
| 22 and 70 | 770 |
| 130 and 61 | 7930 |