Least Common Multiple (LCM) of 48 and 17
The least common multiple (LCM) of 48 and 17 is 816.
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 48 and 17?
First, calculate the GCD of 48 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 17 = 2 remainder 14 |
| 2 | 17 ÷ 14 = 1 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 111 | 5106 |
| 64 and 135 | 8640 |
| 102 and 150 | 2550 |
| 188 and 184 | 8648 |
| 11 and 36 | 396 |