Least Common Multiple (LCM) of 115 and 147
The least common multiple (LCM) of 115 and 147 is 16905.
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 147?
First, calculate the GCD of 115 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 147 = 0 remainder 115 |
| 2 | 147 ÷ 115 = 1 remainder 32 |
| 3 | 115 ÷ 32 = 3 remainder 19 |
| 4 | 32 ÷ 19 = 1 remainder 13 |
| 5 | 19 ÷ 13 = 1 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 51 | 1785 |
| 33 and 51 | 561 |
| 113 and 113 | 113 |
| 84 and 105 | 420 |
| 33 and 30 | 330 |