Least Common Multiple (LCM) of 71 and 25
The least common multiple (LCM) of 71 and 25 is 1775.
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 25?
First, calculate the GCD of 71 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 25 = 2 remainder 21 |
| 2 | 25 ÷ 21 = 1 remainder 4 |
| 3 | 21 ÷ 4 = 5 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 165 | 990 |
| 120 and 155 | 3720 |
| 27 and 40 | 1080 |
| 46 and 109 | 5014 |
| 25 and 180 | 900 |