Least Common Multiple (LCM) of 25 and 198
The least common multiple (LCM) of 25 and 198 is 4950.
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 198?
First, calculate the GCD of 25 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 198 = 0 remainder 25 |
| 2 | 198 ÷ 25 = 7 remainder 23 |
| 3 | 25 ÷ 23 = 1 remainder 2 |
| 4 | 23 ÷ 2 = 11 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 55 | 2695 |
| 102 and 126 | 2142 |
| 127 and 174 | 22098 |
| 93 and 55 | 5115 |
| 138 and 198 | 4554 |