Least Common Multiple (LCM) of 83 and 176
The least common multiple (LCM) of 83 and 176 is 14608.
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 83 and 176?
First, calculate the GCD of 83 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 176 = 0 remainder 83 |
| 2 | 176 ÷ 83 = 2 remainder 10 |
| 3 | 83 ÷ 10 = 8 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 198 | 23562 |
| 105 and 135 | 945 |
| 30 and 39 | 390 |
| 183 and 189 | 11529 |
| 160 and 37 | 5920 |