Least Common Multiple (LCM) of 176 and 51
The least common multiple (LCM) of 176 and 51 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 51?
First, calculate the GCD of 176 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 51 = 3 remainder 23 |
| 2 | 51 ÷ 23 = 2 remainder 5 |
| 3 | 23 ÷ 5 = 4 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 200 | 4200 |
| 76 and 14 | 532 |
| 108 and 126 | 756 |
| 52 and 43 | 2236 |
| 138 and 68 | 4692 |