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 |
|---|---|
| 132 and 147 | 6468 |
| 88 and 88 | 88 |
| 154 and 67 | 10318 |
| 142 and 198 | 14058 |
| 143 and 49 | 7007 |