Least Common Multiple (LCM) of 163 and 135
The least common multiple (LCM) of 163 and 135 is 22005.
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 135?
First, calculate the GCD of 163 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 135 = 1 remainder 28 |
| 2 | 135 ÷ 28 = 4 remainder 23 |
| 3 | 28 ÷ 23 = 1 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 105 | 11445 |
| 66 and 74 | 2442 |
| 107 and 77 | 8239 |
| 70 and 58 | 2030 |
| 153 and 75 | 3825 |