Least Common Multiple (LCM) of 54 and 197
The least common multiple (LCM) of 54 and 197 is 10638.
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 197?
First, calculate the GCD of 54 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 197 = 0 remainder 54 |
| 2 | 197 ÷ 54 = 3 remainder 35 |
| 3 | 54 ÷ 35 = 1 remainder 19 |
| 4 | 35 ÷ 19 = 1 remainder 16 |
| 5 | 19 ÷ 16 = 1 remainder 3 |
| 6 | 16 ÷ 3 = 5 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 200 | 10600 |
| 83 and 176 | 14608 |
| 198 and 24 | 792 |
| 63 and 128 | 8064 |
| 79 and 128 | 10112 |