Least Common Multiple (LCM) of 51 and 131
The least common multiple (LCM) of 51 and 131 is 6681.
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 51 and 131?
First, calculate the GCD of 51 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 131 = 0 remainder 51 |
| 2 | 131 ÷ 51 = 2 remainder 29 |
| 3 | 51 ÷ 29 = 1 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 39 | 1248 |
| 175 and 15 | 525 |
| 152 and 115 | 17480 |
| 162 and 28 | 2268 |
| 185 and 69 | 12765 |