Least Common Multiple (LCM) of 108 and 47
The least common multiple (LCM) of 108 and 47 is 5076.
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 108 and 47?
First, calculate the GCD of 108 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 47 = 2 remainder 14 |
| 2 | 47 ÷ 14 = 3 remainder 5 |
| 3 | 14 ÷ 5 = 2 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 118 | 7906 |
| 54 and 167 | 9018 |
| 108 and 126 | 756 |
| 188 and 27 | 5076 |
| 146 and 147 | 21462 |