Least Common Multiple (LCM) of 48 and 165
The least common multiple (LCM) of 48 and 165 is 2640.
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 165?
First, calculate the GCD of 48 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 165 = 0 remainder 48 |
| 2 | 165 ÷ 48 = 3 remainder 21 |
| 3 | 48 ÷ 21 = 2 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 85 | 4505 |
| 106 and 29 | 3074 |
| 170 and 68 | 340 |
| 65 and 144 | 9360 |
| 144 and 82 | 5904 |