Least Common Multiple (LCM) of 113 and 165
The least common multiple (LCM) of 113 and 165 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 113 and 165?
First, calculate the GCD of 113 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 165 = 0 remainder 113 |
| 2 | 165 ÷ 113 = 1 remainder 52 |
| 3 | 113 ÷ 52 = 2 remainder 9 |
| 4 | 52 ÷ 9 = 5 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 147 | 27636 |
| 40 and 172 | 1720 |
| 176 and 74 | 6512 |
| 131 and 172 | 22532 |
| 59 and 192 | 11328 |