Least Common Multiple (LCM) of 196 and 43
The least common multiple (LCM) of 196 and 43 is 8428.
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 43?
First, calculate the GCD of 196 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 43 = 4 remainder 24 |
| 2 | 43 ÷ 24 = 1 remainder 19 |
| 3 | 24 ÷ 19 = 1 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 157 | 28888 |
| 120 and 125 | 3000 |
| 21 and 26 | 546 |
| 188 and 12 | 564 |
| 150 and 111 | 5550 |