Least Common Multiple (LCM) of 54 and 121
The least common multiple (LCM) of 54 and 121 is 6534.
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 121?
First, calculate the GCD of 54 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 121 = 0 remainder 54 |
| 2 | 121 ÷ 54 = 2 remainder 13 |
| 3 | 54 ÷ 13 = 4 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 70 | 630 |
| 123 and 123 | 123 |
| 130 and 168 | 10920 |
| 96 and 121 | 11616 |
| 41 and 34 | 1394 |