Least Common Multiple (LCM) of 32 and 115
The least common multiple (LCM) of 32 and 115 is 3680.
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 32 and 115?
First, calculate the GCD of 32 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 115 = 0 remainder 32 |
| 2 | 115 ÷ 32 = 3 remainder 19 |
| 3 | 32 ÷ 19 = 1 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 16 | 1136 |
| 98 and 48 | 2352 |
| 178 and 35 | 6230 |
| 65 and 113 | 7345 |
| 11 and 31 | 341 |