Least Common Multiple (LCM) of 56 and 97
The least common multiple (LCM) of 56 and 97 is 5432.
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 97?
First, calculate the GCD of 56 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 97 = 0 remainder 56 |
| 2 | 97 ÷ 56 = 1 remainder 41 |
| 3 | 56 ÷ 41 = 1 remainder 15 |
| 4 | 41 ÷ 15 = 2 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 26 | 1586 |
| 20 and 83 | 1660 |
| 77 and 111 | 8547 |
| 191 and 83 | 15853 |
| 131 and 46 | 6026 |