Least Common Multiple (LCM) of 54 and 97
The least common multiple (LCM) of 54 and 97 is 5238.
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 54 and 97?
First, calculate the GCD of 54 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 97 = 0 remainder 54 |
| 2 | 97 ÷ 54 = 1 remainder 43 |
| 3 | 54 ÷ 43 = 1 remainder 11 |
| 4 | 43 ÷ 11 = 3 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 89 | 10858 |
| 50 and 89 | 4450 |
| 169 and 100 | 16900 |
| 155 and 92 | 14260 |
| 57 and 177 | 3363 |