Least Common Multiple (LCM) of 196 and 143
The least common multiple (LCM) of 196 and 143 is 28028.
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 143?
First, calculate the GCD of 196 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 143 = 1 remainder 53 |
| 2 | 143 ÷ 53 = 2 remainder 37 |
| 3 | 53 ÷ 37 = 1 remainder 16 |
| 4 | 37 ÷ 16 = 2 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 81 | 324 |
| 112 and 189 | 3024 |
| 40 and 109 | 4360 |
| 117 and 47 | 5499 |
| 126 and 155 | 19530 |