Least Common Multiple (LCM) of 126 and 47
The least common multiple (LCM) of 126 and 47 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 126 and 47?
First, calculate the GCD of 126 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 47 = 2 remainder 32 |
| 2 | 47 ÷ 32 = 1 remainder 15 |
| 3 | 32 ÷ 15 = 2 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 105 | 4620 |
| 169 and 26 | 338 |
| 40 and 111 | 4440 |
| 45 and 199 | 8955 |
| 76 and 155 | 11780 |