Least Common Multiple (LCM) of 176 and 189
The least common multiple (LCM) of 176 and 189 is 33264.
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 176 and 189?
First, calculate the GCD of 176 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 189 = 0 remainder 176 |
| 2 | 189 ÷ 176 = 1 remainder 13 |
| 3 | 176 ÷ 13 = 13 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 120 | 240 |
| 63 and 171 | 1197 |
| 87 and 175 | 15225 |
| 10 and 94 | 470 |
| 185 and 107 | 19795 |