Least Common Multiple (LCM) of 131 and 54
The least common multiple (LCM) of 131 and 54 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 131 and 54?
First, calculate the GCD of 131 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 54 = 2 remainder 23 |
| 2 | 54 ÷ 23 = 2 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 28 | 5236 |
| 145 and 143 | 20735 |
| 52 and 150 | 3900 |
| 121 and 116 | 14036 |
| 180 and 21 | 1260 |