Least Common Multiple (LCM) of 113 and 25
The least common multiple (LCM) of 113 and 25 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 113 and 25?
First, calculate the GCD of 113 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 25 = 4 remainder 13 |
| 2 | 25 ÷ 13 = 1 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 135 | 4590 |
| 49 and 89 | 4361 |
| 167 and 178 | 29726 |
| 17 and 88 | 1496 |
| 142 and 53 | 7526 |