Least Common Multiple (LCM) of 97 and 56
The least common multiple (LCM) of 97 and 56 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 97 and 56?
First, calculate the GCD of 97 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 56 = 1 remainder 41 |
| 2 | 56 ÷ 41 = 1 remainder 15 |
| 3 | 41 ÷ 15 = 2 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 51 | 8619 |
| 152 and 57 | 456 |
| 111 and 115 | 12765 |
| 77 and 137 | 10549 |
| 119 and 80 | 9520 |