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 |
|---|---|
| 111 and 158 | 17538 |
| 122 and 107 | 13054 |
| 170 and 146 | 12410 |
| 90 and 160 | 1440 |
| 12 and 135 | 540 |