Least Common Multiple (LCM) of 172 and 193
The least common multiple (LCM) of 172 and 193 is 33196.
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 193?
First, calculate the GCD of 172 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 193 = 0 remainder 172 |
| 2 | 193 ÷ 172 = 1 remainder 21 |
| 3 | 172 ÷ 21 = 8 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 29 | 3857 |
| 83 and 29 | 2407 |
| 67 and 70 | 4690 |
| 188 and 63 | 11844 |
| 144 and 141 | 6768 |