Least Common Multiple (LCM) of 51 and 176
The least common multiple (LCM) of 51 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 51 and 176?
First, calculate the GCD of 51 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 176 = 0 remainder 51 |
| 2 | 176 ÷ 51 = 3 remainder 23 |
| 3 | 51 ÷ 23 = 2 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 69 | 5865 |
| 50 and 142 | 3550 |
| 144 and 189 | 3024 |
| 52 and 137 | 7124 |
| 120 and 112 | 1680 |