Least Common Multiple (LCM) of 162 and 45
The least common multiple (LCM) of 162 and 45 is 810.
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 162 and 45?
First, calculate the GCD of 162 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 45 = 3 remainder 27 |
| 2 | 45 ÷ 27 = 1 remainder 18 |
| 3 | 27 ÷ 18 = 1 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 23 | 230 |
| 123 and 29 | 3567 |
| 85 and 66 | 5610 |
| 112 and 153 | 17136 |
| 100 and 50 | 100 |