Least Common Multiple (LCM) of 163 and 195
The least common multiple (LCM) of 163 and 195 is 31785.
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 195?
First, calculate the GCD of 163 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 195 = 0 remainder 163 |
| 2 | 195 ÷ 163 = 1 remainder 32 |
| 3 | 163 ÷ 32 = 5 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 196 | 1764 |
| 63 and 106 | 6678 |
| 112 and 16 | 112 |
| 128 and 155 | 19840 |
| 184 and 10 | 920 |