Least Common Multiple (LCM) of 110 and 162
The least common multiple (LCM) of 110 and 162 is 8910.
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 110 and 162?
First, calculate the GCD of 110 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 162 = 0 remainder 110 |
| 2 | 162 ÷ 110 = 1 remainder 52 |
| 3 | 110 ÷ 52 = 2 remainder 6 |
| 4 | 52 ÷ 6 = 8 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 44 | 4532 |
| 170 and 51 | 510 |
| 133 and 43 | 5719 |
| 26 and 83 | 2158 |
| 91 and 90 | 8190 |