Least Common Multiple (LCM) of 46 and 126
The least common multiple (LCM) of 46 and 126 is 2898.
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 126?
First, calculate the GCD of 46 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 126 = 0 remainder 46 |
| 2 | 126 ÷ 46 = 2 remainder 34 |
| 3 | 46 ÷ 34 = 1 remainder 12 |
| 4 | 34 ÷ 12 = 2 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 142 | 8094 |
| 55 and 66 | 330 |
| 122 and 77 | 9394 |
| 13 and 106 | 1378 |
| 13 and 11 | 143 |