Least Common Multiple (LCM) of 176 and 102
The least common multiple (LCM) of 176 and 102 is 8976.
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 102?
First, calculate the GCD of 176 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 102 = 1 remainder 74 |
| 2 | 102 ÷ 74 = 1 remainder 28 |
| 3 | 74 ÷ 28 = 2 remainder 18 |
| 4 | 28 ÷ 18 = 1 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 100 | 1300 |
| 36 and 141 | 1692 |
| 48 and 90 | 720 |
| 149 and 84 | 12516 |
| 185 and 152 | 28120 |