Least Common Multiple (LCM) of 51 and 115
The least common multiple (LCM) of 51 and 115 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 51 and 115?
First, calculate the GCD of 51 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 115 = 0 remainder 51 |
| 2 | 115 ÷ 51 = 2 remainder 13 |
| 3 | 51 ÷ 13 = 3 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 23 | 4071 |
| 169 and 189 | 31941 |
| 148 and 159 | 23532 |
| 129 and 14 | 1806 |
| 72 and 75 | 1800 |