Least Common Multiple (LCM) of 25 and 96
The least common multiple (LCM) of 25 and 96 is 2400.
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 96?
First, calculate the GCD of 25 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 96 = 0 remainder 25 |
| 2 | 96 ÷ 25 = 3 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 |
|---|---|
| 105 and 74 | 7770 |
| 110 and 170 | 1870 |
| 65 and 141 | 9165 |
| 145 and 99 | 14355 |
| 94 and 175 | 16450 |