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 |
|---|---|
| 184 and 198 | 18216 |
| 154 and 128 | 9856 |
| 112 and 124 | 3472 |
| 180 and 94 | 8460 |
| 53 and 196 | 10388 |