Least Common Multiple (LCM) of 109 and 47
The least common multiple (LCM) of 109 and 47 is 5123.
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 109 and 47?
First, calculate the GCD of 109 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 47 = 2 remainder 15 |
| 2 | 47 ÷ 15 = 3 remainder 2 |
| 3 | 15 ÷ 2 = 7 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 189 | 2079 |
| 78 and 81 | 2106 |
| 132 and 156 | 1716 |
| 38 and 128 | 2432 |
| 109 and 155 | 16895 |