Least Common Multiple (LCM) of 105 and 176
The least common multiple (LCM) of 105 and 176 is 18480.
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 105 and 176?
First, calculate the GCD of 105 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 176 = 0 remainder 105 |
| 2 | 176 ÷ 105 = 1 remainder 71 |
| 3 | 105 ÷ 71 = 1 remainder 34 |
| 4 | 71 ÷ 34 = 2 remainder 3 |
| 5 | 34 ÷ 3 = 11 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 117 | 6903 |
| 144 and 138 | 3312 |
| 96 and 188 | 4512 |
| 105 and 38 | 3990 |
| 58 and 80 | 2320 |