Least Common Multiple (LCM) of 50 and 17
The least common multiple (LCM) of 50 and 17 is 850.
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 17?
First, calculate the GCD of 50 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 17 = 2 remainder 16 |
| 2 | 17 ÷ 16 = 1 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 172 | 12212 |
| 133 and 180 | 23940 |
| 104 and 112 | 1456 |
| 192 and 142 | 13632 |
| 100 and 53 | 5300 |