Least Common Multiple (LCM) of 47 and 85
The least common multiple (LCM) of 47 and 85 is 3995.
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 85?
First, calculate the GCD of 47 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 85 = 0 remainder 47 |
| 2 | 85 ÷ 47 = 1 remainder 38 |
| 3 | 47 ÷ 38 = 1 remainder 9 |
| 4 | 38 ÷ 9 = 4 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 192 | 4416 |
| 34 and 47 | 1598 |
| 157 and 35 | 5495 |
| 25 and 61 | 1525 |
| 117 and 101 | 11817 |