Least Common Multiple (LCM) of 178 and 56
The least common multiple (LCM) of 178 and 56 is 4984.
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 178 and 56?
First, calculate the GCD of 178 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 56 = 3 remainder 10 |
| 2 | 56 ÷ 10 = 5 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 105 | 1050 |
| 73 and 49 | 3577 |
| 138 and 189 | 8694 |
| 80 and 89 | 7120 |
| 34 and 163 | 5542 |