Least Common Multiple (LCM) of 178 and 50
The least common multiple (LCM) of 178 and 50 is 4450.
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 50?
First, calculate the GCD of 178 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 50 = 3 remainder 28 |
| 2 | 50 ÷ 28 = 1 remainder 22 |
| 3 | 28 ÷ 22 = 1 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 105 | 11445 |
| 171 and 71 | 12141 |
| 139 and 28 | 3892 |
| 198 and 12 | 396 |
| 24 and 17 | 408 |