Least Common Multiple (LCM) of 25 and 196
The least common multiple (LCM) of 25 and 196 is 4900.
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 196?
First, calculate the GCD of 25 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 196 = 0 remainder 25 |
| 2 | 196 ÷ 25 = 7 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 |
|---|---|
| 96 and 52 | 1248 |
| 28 and 119 | 476 |
| 113 and 28 | 3164 |
| 74 and 187 | 13838 |
| 149 and 197 | 29353 |