Least Common Multiple (LCM) of 10 and 25
The least common multiple (LCM) of 10 and 25 is 50.
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 10 and 25?
First, calculate the GCD of 10 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 25 = 0 remainder 10 |
| 2 | 25 ÷ 10 = 2 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 190 | 30210 |
| 164 and 114 | 9348 |
| 189 and 89 | 16821 |
| 140 and 39 | 5460 |
| 74 and 122 | 4514 |