Least Common Multiple (LCM) of 189 and 172
The least common multiple (LCM) of 189 and 172 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 189 and 172?
First, calculate the GCD of 189 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 172 = 1 remainder 17 |
| 2 | 172 ÷ 17 = 10 remainder 2 |
| 3 | 17 ÷ 2 = 8 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 26 | 1950 |
| 112 and 136 | 1904 |
| 150 and 127 | 19050 |
| 184 and 13 | 2392 |
| 38 and 23 | 874 |