Least Common Multiple (LCM) of 47 and 159
The least common multiple (LCM) of 47 and 159 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 47 and 159?
First, calculate the GCD of 47 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 159 = 0 remainder 47 |
| 2 | 159 ÷ 47 = 3 remainder 18 |
| 3 | 47 ÷ 18 = 2 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 97 | 12319 |
| 62 and 22 | 682 |
| 81 and 52 | 4212 |
| 47 and 159 | 7473 |
| 186 and 145 | 26970 |