Least Common Multiple (LCM) of 49 and 17
The least common multiple (LCM) of 49 and 17 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 49 and 17?
First, calculate the GCD of 49 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 17 = 2 remainder 15 |
| 2 | 17 ÷ 15 = 1 remainder 2 |
| 3 | 15 ÷ 2 = 7 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 64 | 6464 |
| 186 and 174 | 5394 |
| 24 and 42 | 168 |
| 17 and 150 | 2550 |
| 200 and 14 | 1400 |