Least Common Multiple (LCM) of 75 and 196
The least common multiple (LCM) of 75 and 196 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 75 and 196?
First, calculate the GCD of 75 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 196 = 0 remainder 75 |
| 2 | 196 ÷ 75 = 2 remainder 46 |
| 3 | 75 ÷ 46 = 1 remainder 29 |
| 4 | 46 ÷ 29 = 1 remainder 17 |
| 5 | 29 ÷ 17 = 1 remainder 12 |
| 6 | 17 ÷ 12 = 1 remainder 5 |
| 7 | 12 ÷ 5 = 2 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 108 | 756 |
| 78 and 101 | 7878 |
| 150 and 75 | 150 |
| 167 and 133 | 22211 |
| 97 and 92 | 8924 |