Least Common Multiple (LCM) of 54 and 146
The least common multiple (LCM) of 54 and 146 is 3942.
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 146?
First, calculate the GCD of 54 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 146 = 0 remainder 54 |
| 2 | 146 ÷ 54 = 2 remainder 38 |
| 3 | 54 ÷ 38 = 1 remainder 16 |
| 4 | 38 ÷ 16 = 2 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 132 | 2772 |
| 172 and 99 | 17028 |
| 121 and 19 | 2299 |
| 196 and 142 | 13916 |
| 179 and 136 | 24344 |