Least Common Multiple (LCM) of 176 and 196
The least common multiple (LCM) of 176 and 196 is 8624.
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 196?
First, calculate the GCD of 176 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 196 = 0 remainder 176 |
| 2 | 196 ÷ 176 = 1 remainder 20 |
| 3 | 176 ÷ 20 = 8 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 109 | 6540 |
| 43 and 142 | 6106 |
| 15 and 199 | 2985 |
| 17 and 185 | 3145 |
| 137 and 80 | 10960 |