Least Common Multiple (LCM) of 17 and 49
The least common multiple (LCM) of 17 and 49 is 833.
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 17 and 49?
First, calculate the GCD of 17 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 49 = 0 remainder 17 |
| 2 | 49 ÷ 17 = 2 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 19 | 3192 |
| 103 and 24 | 2472 |
| 128 and 164 | 5248 |
| 148 and 131 | 19388 |
| 75 and 133 | 9975 |