Least Common Multiple (LCM) of 165 and 113
The least common multiple (LCM) of 165 and 113 is 18645.
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 113?
First, calculate the GCD of 165 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 113 = 1 remainder 52 |
| 2 | 113 ÷ 52 = 2 remainder 9 |
| 3 | 52 ÷ 9 = 5 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 140 | 24220 |
| 34 and 89 | 3026 |
| 21 and 89 | 1869 |
| 193 and 133 | 25669 |
| 171 and 47 | 8037 |