Least Common Multiple (LCM) of 55 and 146
The least common multiple (LCM) of 55 and 146 is 8030.
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 55 and 146?
First, calculate the GCD of 55 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 146 = 0 remainder 55 |
| 2 | 146 ÷ 55 = 2 remainder 36 |
| 3 | 55 ÷ 36 = 1 remainder 19 |
| 4 | 36 ÷ 19 = 1 remainder 17 |
| 5 | 19 ÷ 17 = 1 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 144 | 8496 |
| 13 and 32 | 416 |
| 56 and 144 | 1008 |
| 172 and 136 | 5848 |
| 105 and 147 | 735 |