Least Common Multiple (LCM) of 54 and 47
The least common multiple (LCM) of 54 and 47 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 54 and 47?
First, calculate the GCD of 54 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 47 = 1 remainder 7 |
| 2 | 47 ÷ 7 = 6 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 35 | 3710 |
| 19 and 98 | 1862 |
| 121 and 96 | 11616 |
| 156 and 196 | 7644 |
| 151 and 83 | 12533 |