Least Common Multiple (LCM) of 48 and 65
The least common multiple (LCM) of 48 and 65 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 48 and 65?
First, calculate the GCD of 48 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 65 = 0 remainder 48 |
| 2 | 65 ÷ 48 = 1 remainder 17 |
| 3 | 48 ÷ 17 = 2 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 57 | 6270 |
| 175 and 102 | 17850 |
| 108 and 128 | 3456 |
| 41 and 59 | 2419 |
| 24 and 57 | 456 |