Least Common Multiple (LCM) of 54 and 131
The least common multiple (LCM) of 54 and 131 is 7074.
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 131?
First, calculate the GCD of 54 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 131 = 0 remainder 54 |
| 2 | 131 ÷ 54 = 2 remainder 23 |
| 3 | 54 ÷ 23 = 2 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 76 | 13148 |
| 91 and 79 | 7189 |
| 120 and 144 | 720 |
| 68 and 142 | 4828 |
| 48 and 70 | 1680 |