Least Common Multiple (LCM) of 55 and 131
The least common multiple (LCM) of 55 and 131 is 7205.
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 55 and 131?
First, calculate the GCD of 55 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 131 = 0 remainder 55 |
| 2 | 131 ÷ 55 = 2 remainder 21 |
| 3 | 55 ÷ 21 = 2 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 27 | 1242 |
| 142 and 112 | 7952 |
| 22 and 200 | 2200 |
| 132 and 141 | 6204 |
| 145 and 193 | 27985 |