Least Common Multiple (LCM) of 105 and 146
The least common multiple (LCM) of 105 and 146 is 15330.
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 105 and 146?
First, calculate the GCD of 105 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 146 = 0 remainder 105 |
| 2 | 146 ÷ 105 = 1 remainder 41 |
| 3 | 105 ÷ 41 = 2 remainder 23 |
| 4 | 41 ÷ 23 = 1 remainder 18 |
| 5 | 23 ÷ 18 = 1 remainder 5 |
| 6 | 18 ÷ 5 = 3 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 53 | 4505 |
| 107 and 68 | 7276 |
| 103 and 52 | 5356 |
| 128 and 95 | 12160 |
| 102 and 26 | 1326 |