Least Common Multiple (LCM) of 47 and 89
The least common multiple (LCM) of 47 and 89 is 4183.
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 89?
First, calculate the GCD of 47 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 89 = 0 remainder 47 |
| 2 | 89 ÷ 47 = 1 remainder 42 |
| 3 | 47 ÷ 42 = 1 remainder 5 |
| 4 | 42 ÷ 5 = 8 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 39 | 2184 |
| 39 and 184 | 7176 |
| 35 and 10 | 70 |
| 57 and 27 | 513 |
| 115 and 122 | 14030 |