Least Common Multiple (LCM) of 35 and 163
The least common multiple (LCM) of 35 and 163 is 5705.
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 35 and 163?
First, calculate the GCD of 35 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 163 = 0 remainder 35 |
| 2 | 163 ÷ 35 = 4 remainder 23 |
| 3 | 35 ÷ 23 = 1 remainder 12 |
| 4 | 23 ÷ 12 = 1 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 121 | 121 |
| 43 and 41 | 1763 |
| 155 and 111 | 17205 |
| 197 and 130 | 25610 |
| 45 and 18 | 90 |