Least Common Multiple (LCM) of 48 and 71
The least common multiple (LCM) of 48 and 71 is 3408.
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 71?
First, calculate the GCD of 48 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 71 = 0 remainder 48 |
| 2 | 71 ÷ 48 = 1 remainder 23 |
| 3 | 48 ÷ 23 = 2 remainder 2 |
| 4 | 23 ÷ 2 = 11 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 25 | 1950 |
| 132 and 197 | 26004 |
| 170 and 123 | 20910 |
| 43 and 190 | 8170 |
| 168 and 140 | 840 |