Least Common Multiple (LCM) of 116 and 159
The least common multiple (LCM) of 116 and 159 is 18444.
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 116 and 159?
First, calculate the GCD of 116 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 159 = 0 remainder 116 |
| 2 | 159 ÷ 116 = 1 remainder 43 |
| 3 | 116 ÷ 43 = 2 remainder 30 |
| 4 | 43 ÷ 30 = 1 remainder 13 |
| 5 | 30 ÷ 13 = 2 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 171 | 3420 |
| 58 and 74 | 2146 |
| 96 and 183 | 5856 |
| 37 and 105 | 3885 |
| 31 and 100 | 3100 |