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 |
|---|---|
| 73 and 113 | 8249 |
| 81 and 181 | 14661 |
| 13 and 13 | 13 |
| 175 and 132 | 23100 |
| 125 and 104 | 13000 |