Least Common Multiple (LCM) of 46 and 105
The least common multiple (LCM) of 46 and 105 is 4830.
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 46 and 105?
First, calculate the GCD of 46 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 105 = 0 remainder 46 |
| 2 | 105 ÷ 46 = 2 remainder 13 |
| 3 | 46 ÷ 13 = 3 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 179 | 12351 |
| 20 and 77 | 1540 |
| 190 and 162 | 15390 |
| 106 and 61 | 6466 |
| 62 and 26 | 806 |