Least Common Multiple (LCM) of 47 and 107
The least common multiple (LCM) of 47 and 107 is 5029.
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 107?
First, calculate the GCD of 47 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 107 = 0 remainder 47 |
| 2 | 107 ÷ 47 = 2 remainder 13 |
| 3 | 47 ÷ 13 = 3 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 104 | 5720 |
| 183 and 120 | 7320 |
| 132 and 46 | 3036 |
| 117 and 164 | 19188 |
| 108 and 17 | 1836 |