Least Common Multiple (LCM) of 24 and 115
The least common multiple (LCM) of 24 and 115 is 2760.
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 24 and 115?
First, calculate the GCD of 24 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 115 = 0 remainder 24 |
| 2 | 115 ÷ 24 = 4 remainder 19 |
| 3 | 24 ÷ 19 = 1 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 180 | 7380 |
| 74 and 101 | 7474 |
| 179 and 73 | 13067 |
| 161 and 132 | 21252 |
| 29 and 115 | 3335 |