Least Common Multiple (LCM) of 47 and 126
The least common multiple (LCM) of 47 and 126 is 5922.
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 47 and 126?
First, calculate the GCD of 47 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 126 = 0 remainder 47 |
| 2 | 126 ÷ 47 = 2 remainder 32 |
| 3 | 47 ÷ 32 = 1 remainder 15 |
| 4 | 32 ÷ 15 = 2 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 80 | 2160 |
| 63 and 20 | 1260 |
| 89 and 130 | 11570 |
| 38 and 143 | 5434 |
| 126 and 121 | 15246 |