Least Common Multiple (LCM) of 57 and 176
The least common multiple (LCM) of 57 and 176 is 10032.
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 57 and 176?
First, calculate the GCD of 57 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 176 = 0 remainder 57 |
| 2 | 176 ÷ 57 = 3 remainder 5 |
| 3 | 57 ÷ 5 = 11 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 80 | 5680 |
| 170 and 109 | 18530 |
| 189 and 21 | 189 |
| 11 and 94 | 1034 |
| 141 and 69 | 3243 |