Least Common Multiple (LCM) of 196 and 75
The least common multiple (LCM) of 196 and 75 is 14700.
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 75?
First, calculate the GCD of 196 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 75 = 2 remainder 46 |
| 2 | 75 ÷ 46 = 1 remainder 29 |
| 3 | 46 ÷ 29 = 1 remainder 17 |
| 4 | 29 ÷ 17 = 1 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 172 | 5504 |
| 142 and 172 | 12212 |
| 49 and 124 | 6076 |
| 14 and 27 | 378 |
| 165 and 65 | 2145 |