Least Common Multiple (LCM) of 56 and 197
The least common multiple (LCM) of 56 and 197 is 11032.
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 56 and 197?
First, calculate the GCD of 56 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 197 = 0 remainder 56 |
| 2 | 197 ÷ 56 = 3 remainder 29 |
| 3 | 56 ÷ 29 = 1 remainder 27 |
| 4 | 29 ÷ 27 = 1 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 29 | 3915 |
| 182 and 58 | 5278 |
| 69 and 82 | 5658 |
| 15 and 109 | 1635 |
| 54 and 172 | 4644 |