Least Common Multiple (LCM) of 163 and 100
The least common multiple (LCM) of 163 and 100 is 16300.
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 100?
First, calculate the GCD of 163 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 100 = 1 remainder 63 |
| 2 | 100 ÷ 63 = 1 remainder 37 |
| 3 | 63 ÷ 37 = 1 remainder 26 |
| 4 | 37 ÷ 26 = 1 remainder 11 |
| 5 | 26 ÷ 11 = 2 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 23 | 2231 |
| 68 and 75 | 5100 |
| 115 and 27 | 3105 |
| 151 and 142 | 21442 |
| 38 and 133 | 266 |