Least Common Multiple (LCM) of 43 and 165
The least common multiple (LCM) of 43 and 165 is 7095.
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 43 and 165?
First, calculate the GCD of 43 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 165 = 0 remainder 43 |
| 2 | 165 ÷ 43 = 3 remainder 36 |
| 3 | 43 ÷ 36 = 1 remainder 7 |
| 4 | 36 ÷ 7 = 5 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 92 | 2484 |
| 177 and 75 | 4425 |
| 61 and 198 | 12078 |
| 80 and 131 | 10480 |
| 23 and 58 | 1334 |