Least Common Multiple (LCM) of 25 and 113
The least common multiple (LCM) of 25 and 113 is 2825.
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 113?
First, calculate the GCD of 25 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 113 = 0 remainder 25 |
| 2 | 113 ÷ 25 = 4 remainder 13 |
| 3 | 25 ÷ 13 = 1 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 42 | 2856 |
| 152 and 34 | 2584 |
| 133 and 25 | 3325 |
| 48 and 131 | 6288 |
| 77 and 93 | 7161 |