Least Common Multiple (LCM) of 115 and 51
The least common multiple (LCM) of 115 and 51 is 5865.
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 115 and 51?
First, calculate the GCD of 115 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 51 = 2 remainder 13 |
| 2 | 51 ÷ 13 = 3 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 61 | 10980 |
| 123 and 117 | 4797 |
| 132 and 45 | 1980 |
| 47 and 131 | 6157 |
| 122 and 13 | 1586 |