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 |
|---|---|
| 47 and 23 | 1081 |
| 22 and 66 | 66 |
| 137 and 58 | 7946 |
| 10 and 80 | 80 |
| 141 and 30 | 1410 |