Least Common Multiple (LCM) of 50 and 178
The least common multiple (LCM) of 50 and 178 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 50 and 178?
First, calculate the GCD of 50 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 178 = 0 remainder 50 |
| 2 | 178 ÷ 50 = 3 remainder 28 |
| 3 | 50 ÷ 28 = 1 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 26 | 3562 |
| 100 and 112 | 2800 |
| 35 and 173 | 6055 |
| 56 and 106 | 2968 |
| 33 and 99 | 99 |