Least Common Multiple (LCM) of 176 and 195
The least common multiple (LCM) of 176 and 195 is 34320.
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 195?
First, calculate the GCD of 176 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 195 = 0 remainder 176 |
| 2 | 195 ÷ 176 = 1 remainder 19 |
| 3 | 176 ÷ 19 = 9 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 117 | 1287 |
| 80 and 119 | 9520 |
| 47 and 164 | 7708 |
| 146 and 192 | 14016 |
| 196 and 199 | 39004 |