Least Common Multiple (LCM) of 54 and 122
The least common multiple (LCM) of 54 and 122 is 3294.
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 122?
First, calculate the GCD of 54 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 122 = 0 remainder 54 |
| 2 | 122 ÷ 54 = 2 remainder 14 |
| 3 | 54 ÷ 14 = 3 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 29 | 3103 |
| 12 and 79 | 948 |
| 34 and 14 | 238 |
| 31 and 103 | 3193 |
| 200 and 172 | 8600 |