Least Common Multiple (LCM) of 172 and 197
The least common multiple (LCM) of 172 and 197 is 33884.
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 172 and 197?
First, calculate the GCD of 172 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 197 = 0 remainder 172 |
| 2 | 197 ÷ 172 = 1 remainder 25 |
| 3 | 172 ÷ 25 = 6 remainder 22 |
| 4 | 25 ÷ 22 = 1 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 95 | 1710 |
| 22 and 19 | 418 |
| 178 and 170 | 15130 |
| 105 and 125 | 2625 |
| 149 and 30 | 4470 |