Least Common Multiple (LCM) of 111 and 162
The least common multiple (LCM) of 111 and 162 is 5994.
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 111 and 162?
First, calculate the GCD of 111 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 162 = 0 remainder 111 |
| 2 | 162 ÷ 111 = 1 remainder 51 |
| 3 | 111 ÷ 51 = 2 remainder 9 |
| 4 | 51 ÷ 9 = 5 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 84 | 7980 |
| 74 and 78 | 2886 |
| 173 and 49 | 8477 |
| 126 and 117 | 1638 |
| 68 and 178 | 6052 |