Least Common Multiple (LCM) of 165 and 47
The least common multiple (LCM) of 165 and 47 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 165 and 47?
First, calculate the GCD of 165 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 47 = 3 remainder 24 |
| 2 | 47 ÷ 24 = 1 remainder 23 |
| 3 | 24 ÷ 23 = 1 remainder 1 |
| 4 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 39 | 7527 |
| 135 and 109 | 14715 |
| 133 and 153 | 20349 |
| 174 and 39 | 2262 |
| 28 and 16 | 112 |