Least Common Multiple (LCM) of 176 and 193
The least common multiple (LCM) of 176 and 193 is 33968.
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 193?
First, calculate the GCD of 176 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 193 = 0 remainder 176 |
| 2 | 193 ÷ 176 = 1 remainder 17 |
| 3 | 176 ÷ 17 = 10 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 146 | 11972 |
| 78 and 88 | 3432 |
| 96 and 62 | 2976 |
| 141 and 20 | 2820 |
| 145 and 21 | 3045 |