Least Common Multiple (LCM) of 47 and 165
The least common multiple (LCM) of 47 and 165 is 7755.
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 165?
First, calculate the GCD of 47 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 165 = 0 remainder 47 |
| 2 | 165 ÷ 47 = 3 remainder 24 |
| 3 | 47 ÷ 24 = 1 remainder 23 |
| 4 | 24 ÷ 23 = 1 remainder 1 |
| 5 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 198 | 5544 |
| 66 and 96 | 1056 |
| 83 and 160 | 13280 |
| 69 and 143 | 9867 |
| 31 and 186 | 186 |