Least Common Multiple (LCM) of 48 and 85
The least common multiple (LCM) of 48 and 85 is 4080.
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 85?
First, calculate the GCD of 48 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 85 = 0 remainder 48 |
| 2 | 85 ÷ 48 = 1 remainder 37 |
| 3 | 48 ÷ 37 = 1 remainder 11 |
| 4 | 37 ÷ 11 = 3 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 35 | 1295 |
| 26 and 117 | 234 |
| 18 and 132 | 396 |
| 101 and 101 | 101 |
| 186 and 21 | 1302 |