Least Common Multiple (LCM) of 25 and 111
The least common multiple (LCM) of 25 and 111 is 2775.
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 111?
First, calculate the GCD of 25 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 111 = 0 remainder 25 |
| 2 | 111 ÷ 25 = 4 remainder 11 |
| 3 | 25 ÷ 11 = 2 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 119 | 22610 |
| 71 and 96 | 6816 |
| 44 and 187 | 748 |
| 136 and 199 | 27064 |
| 32 and 63 | 2016 |