Least Common Multiple (LCM) of 54 and 137
The least common multiple (LCM) of 54 and 137 is 7398.
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 137?
First, calculate the GCD of 54 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 137 = 0 remainder 54 |
| 2 | 137 ÷ 54 = 2 remainder 29 |
| 3 | 54 ÷ 29 = 1 remainder 25 |
| 4 | 29 ÷ 25 = 1 remainder 4 |
| 5 | 25 ÷ 4 = 6 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 71 | 1491 |
| 177 and 172 | 30444 |
| 67 and 30 | 2010 |
| 176 and 82 | 7216 |
| 182 and 23 | 4186 |