Least Common Multiple (LCM) of 198 and 125
The least common multiple (LCM) of 198 and 125 is 24750.
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 198 and 125?
First, calculate the GCD of 198 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 125 = 1 remainder 73 |
| 2 | 125 ÷ 73 = 1 remainder 52 |
| 3 | 73 ÷ 52 = 1 remainder 21 |
| 4 | 52 ÷ 21 = 2 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 188 | 10340 |
| 25 and 39 | 975 |
| 102 and 98 | 4998 |
| 109 and 66 | 7194 |
| 198 and 98 | 9702 |