Least Common Multiple (LCM) of 102 and 176
The least common multiple (LCM) of 102 and 176 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 102 and 176?
First, calculate the GCD of 102 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 176 = 0 remainder 102 |
| 2 | 176 ÷ 102 = 1 remainder 74 |
| 3 | 102 ÷ 74 = 1 remainder 28 |
| 4 | 74 ÷ 28 = 2 remainder 18 |
| 5 | 28 ÷ 18 = 1 remainder 10 |
| 6 | 18 ÷ 10 = 1 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 38 | 418 |
| 22 and 88 | 88 |
| 106 and 34 | 1802 |
| 107 and 89 | 9523 |
| 198 and 19 | 3762 |