Least Common Multiple (LCM) of 25 and 71
The least common multiple (LCM) of 25 and 71 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 25 and 71?
First, calculate the GCD of 25 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 71 = 0 remainder 25 |
| 2 | 71 ÷ 25 = 2 remainder 21 |
| 3 | 25 ÷ 21 = 1 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 103 | 12978 |
| 143 and 38 | 5434 |
| 160 and 91 | 14560 |
| 35 and 139 | 4865 |
| 145 and 177 | 25665 |