Least Common Multiple (LCM) of 176 and 197
The least common multiple (LCM) of 176 and 197 is 34672.
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 197?
First, calculate the GCD of 176 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 197 = 0 remainder 176 |
| 2 | 197 ÷ 176 = 1 remainder 21 |
| 3 | 176 ÷ 21 = 8 remainder 8 |
| 4 | 21 ÷ 8 = 2 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 71 | 14129 |
| 112 and 20 | 560 |
| 196 and 92 | 4508 |
| 38 and 30 | 570 |
| 78 and 112 | 4368 |