Least Common Multiple (LCM) of 71 and 28
The least common multiple (LCM) of 71 and 28 is 1988.
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 71 and 28?
First, calculate the GCD of 71 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 28 = 2 remainder 15 |
| 2 | 28 ÷ 15 = 1 remainder 13 |
| 3 | 15 ÷ 13 = 1 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 89 | 15308 |
| 48 and 121 | 5808 |
| 197 and 113 | 22261 |
| 161 and 134 | 21574 |
| 36 and 46 | 828 |