Least Common Multiple (LCM) of 159 and 47
The least common multiple (LCM) of 159 and 47 is 7473.
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 47?
First, calculate the GCD of 159 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 47 = 3 remainder 18 |
| 2 | 47 ÷ 18 = 2 remainder 11 |
| 3 | 18 ÷ 11 = 1 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 127 | 24003 |
| 180 and 175 | 6300 |
| 196 and 78 | 7644 |
| 44 and 105 | 4620 |
| 168 and 31 | 5208 |