Least Common Multiple (LCM) of 41 and 196
The least common multiple (LCM) of 41 and 196 is 8036.
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 41 and 196?
First, calculate the GCD of 41 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 196 = 0 remainder 41 |
| 2 | 196 ÷ 41 = 4 remainder 32 |
| 3 | 41 ÷ 32 = 1 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 153 | 19125 |
| 22 and 70 | 770 |
| 188 and 174 | 16356 |
| 188 and 128 | 6016 |
| 109 and 133 | 14497 |