Least Common Multiple (LCM) of 11 and 162
The least common multiple (LCM) of 11 and 162 is 1782.
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 11 and 162?
First, calculate the GCD of 11 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 162 = 0 remainder 11 |
| 2 | 162 ÷ 11 = 14 remainder 8 |
| 3 | 11 ÷ 8 = 1 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 120 | 120 |
| 45 and 67 | 3015 |
| 21 and 43 | 903 |
| 83 and 62 | 5146 |
| 185 and 96 | 17760 |