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 |
|---|---|
| 48 and 97 | 4656 |
| 30 and 29 | 870 |
| 133 and 175 | 3325 |
| 152 and 85 | 12920 |
| 10 and 154 | 770 |