Least Common Multiple (LCM) of 192 and 197
The least common multiple (LCM) of 192 and 197 is 37824.
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 192 and 197?
First, calculate the GCD of 192 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 197 = 0 remainder 192 |
| 2 | 197 ÷ 192 = 1 remainder 5 |
| 3 | 192 ÷ 5 = 38 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 164 | 23124 |
| 142 and 172 | 12212 |
| 172 and 38 | 3268 |
| 153 and 174 | 8874 |
| 166 and 196 | 16268 |