Least Common Multiple (LCM) of 54 and 71
The least common multiple (LCM) of 54 and 71 is 3834.
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 71?
First, calculate the GCD of 54 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 71 = 0 remainder 54 |
| 2 | 71 ÷ 54 = 1 remainder 17 |
| 3 | 54 ÷ 17 = 3 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 53 | 9275 |
| 44 and 130 | 2860 |
| 120 and 192 | 960 |
| 13 and 146 | 1898 |
| 158 and 93 | 14694 |