Least Common Multiple (LCM) of 50 and 72
The least common multiple (LCM) of 50 and 72 is 1800.
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 72?
First, calculate the GCD of 50 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 72 = 0 remainder 50 |
| 2 | 72 ÷ 50 = 1 remainder 22 |
| 3 | 50 ÷ 22 = 2 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 |
|---|---|
| 184 and 60 | 2760 |
| 17 and 149 | 2533 |
| 75 and 38 | 2850 |
| 27 and 191 | 5157 |
| 181 and 14 | 2534 |