Least Common Multiple (LCM) of 25 and 105
The least common multiple (LCM) of 25 and 105 is 525.
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 105?
First, calculate the GCD of 25 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 105 = 0 remainder 25 |
| 2 | 105 ÷ 25 = 4 remainder 5 |
| 3 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 21 | 3171 |
| 54 and 39 | 702 |
| 133 and 84 | 1596 |
| 109 and 104 | 11336 |
| 60 and 16 | 240 |