Least Common Multiple (LCM) of 165 and 116
The least common multiple (LCM) of 165 and 116 is 19140.
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 116?
First, calculate the GCD of 165 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 116 = 1 remainder 49 |
| 2 | 116 ÷ 49 = 2 remainder 18 |
| 3 | 49 ÷ 18 = 2 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 164 | 2132 |
| 192 and 79 | 15168 |
| 183 and 27 | 1647 |
| 123 and 175 | 21525 |
| 117 and 21 | 819 |