Least Common Multiple (LCM) of 172 and 189
The least common multiple (LCM) of 172 and 189 is 32508.
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 189?
First, calculate the GCD of 172 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 189 = 0 remainder 172 |
| 2 | 189 ÷ 172 = 1 remainder 17 |
| 3 | 172 ÷ 17 = 10 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 169 | 2535 |
| 89 and 39 | 3471 |
| 90 and 197 | 17730 |
| 106 and 168 | 8904 |
| 97 and 93 | 9021 |