Least Common Multiple (LCM) of 65 and 48
The least common multiple (LCM) of 65 and 48 is 3120.
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 65 and 48?
First, calculate the GCD of 65 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 48 = 1 remainder 17 |
| 2 | 48 ÷ 17 = 2 remainder 14 |
| 3 | 17 ÷ 14 = 1 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 117 | 117 |
| 57 and 131 | 7467 |
| 175 and 42 | 1050 |
| 184 and 135 | 24840 |
| 163 and 174 | 28362 |