Least Common Multiple (LCM) of 163 and 45
The least common multiple (LCM) of 163 and 45 is 7335.
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 163 and 45?
First, calculate the GCD of 163 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 45 = 3 remainder 28 |
| 2 | 45 ÷ 28 = 1 remainder 17 |
| 3 | 28 ÷ 17 = 1 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 25 | 3400 |
| 82 and 109 | 8938 |
| 111 and 91 | 10101 |
| 59 and 200 | 11800 |
| 20 and 180 | 180 |