Least Common Multiple (LCM) of 163 and 196
The least common multiple (LCM) of 163 and 196 is 31948.
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 196?
First, calculate the GCD of 163 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 196 = 0 remainder 163 |
| 2 | 196 ÷ 163 = 1 remainder 33 |
| 3 | 163 ÷ 33 = 4 remainder 31 |
| 4 | 33 ÷ 31 = 1 remainder 2 |
| 5 | 31 ÷ 2 = 15 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 88 | 1848 |
| 15 and 157 | 2355 |
| 43 and 170 | 7310 |
| 52 and 193 | 10036 |
| 174 and 142 | 12354 |