Least Common Multiple (LCM) of 196 and 125
The least common multiple (LCM) of 196 and 125 is 24500.
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 196 and 125?
First, calculate the GCD of 196 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 125 = 1 remainder 71 |
| 2 | 125 ÷ 71 = 1 remainder 54 |
| 3 | 71 ÷ 54 = 1 remainder 17 |
| 4 | 54 ÷ 17 = 3 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 69 | 12903 |
| 31 and 51 | 1581 |
| 97 and 63 | 6111 |
| 109 and 194 | 21146 |
| 43 and 115 | 4945 |