Least Common Multiple (LCM) of 45 and 163
The least common multiple (LCM) of 45 and 163 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 45 and 163?
First, calculate the GCD of 45 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 163 = 0 remainder 45 |
| 2 | 163 ÷ 45 = 3 remainder 28 |
| 3 | 45 ÷ 28 = 1 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 27 | 162 |
| 35 and 70 | 70 |
| 189 and 99 | 2079 |
| 197 and 187 | 36839 |
| 95 and 96 | 9120 |