Least Common Multiple (LCM) of 47 and 110
The least common multiple (LCM) of 47 and 110 is 5170.
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 110?
First, calculate the GCD of 47 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 110 = 0 remainder 47 |
| 2 | 110 ÷ 47 = 2 remainder 16 |
| 3 | 47 ÷ 16 = 2 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 17 | 510 |
| 61 and 108 | 6588 |
| 154 and 46 | 3542 |
| 50 and 137 | 6850 |
| 109 and 76 | 8284 |