Least Common Multiple (LCM) of 25 and 52
The least common multiple (LCM) of 25 and 52 is 1300.
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 52?
First, calculate the GCD of 25 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 52 = 0 remainder 25 |
| 2 | 52 ÷ 25 = 2 remainder 2 |
| 3 | 25 ÷ 2 = 12 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 196 | 7056 |
| 134 and 194 | 12998 |
| 135 and 80 | 2160 |
| 106 and 39 | 4134 |
| 68 and 30 | 1020 |