Least Common Multiple (LCM) of 47 and 138
The least common multiple (LCM) of 47 and 138 is 6486.
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 138?
First, calculate the GCD of 47 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 138 = 0 remainder 47 |
| 2 | 138 ÷ 47 = 2 remainder 44 |
| 3 | 47 ÷ 44 = 1 remainder 3 |
| 4 | 44 ÷ 3 = 14 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 126 | 25074 |
| 12 and 12 | 12 |
| 157 and 174 | 27318 |
| 70 and 61 | 4270 |
| 154 and 42 | 462 |