Least Common Multiple (LCM) of 63 and 115
The least common multiple (LCM) of 63 and 115 is 7245.
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 63 and 115?
First, calculate the GCD of 63 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 115 = 0 remainder 63 |
| 2 | 115 ÷ 63 = 1 remainder 52 |
| 3 | 63 ÷ 52 = 1 remainder 11 |
| 4 | 52 ÷ 11 = 4 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 167 | 23714 |
| 187 and 104 | 19448 |
| 116 and 131 | 15196 |
| 182 and 103 | 18746 |
| 64 and 181 | 11584 |