Least Common Multiple (LCM) of 47 and 54
The least common multiple (LCM) of 47 and 54 is 2538.
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 54?
First, calculate the GCD of 47 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 54 = 0 remainder 47 |
| 2 | 54 ÷ 47 = 1 remainder 7 |
| 3 | 47 ÷ 7 = 6 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 105 | 2415 |
| 200 and 102 | 10200 |
| 17 and 155 | 2635 |
| 69 and 136 | 9384 |
| 108 and 144 | 432 |