Least Common Multiple (LCM) of 115 and 63
The least common multiple (LCM) of 115 and 63 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 115 and 63?
First, calculate the GCD of 115 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 63 = 1 remainder 52 |
| 2 | 63 ÷ 52 = 1 remainder 11 |
| 3 | 52 ÷ 11 = 4 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 67 | 6834 |
| 122 and 183 | 366 |
| 162 and 136 | 11016 |
| 113 and 55 | 6215 |
| 10 and 84 | 420 |