Least Common Multiple (LCM) of 57 and 178
The least common multiple (LCM) of 57 and 178 is 10146.
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 178?
First, calculate the GCD of 57 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 178 = 0 remainder 57 |
| 2 | 178 ÷ 57 = 3 remainder 7 |
| 3 | 57 ÷ 7 = 8 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 58 | 7714 |
| 189 and 173 | 32697 |
| 164 and 154 | 12628 |
| 135 and 96 | 4320 |
| 81 and 62 | 5022 |