Least Common Multiple (LCM) of 24 and 113
The least common multiple (LCM) of 24 and 113 is 2712.
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 113?
First, calculate the GCD of 24 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 113 = 0 remainder 24 |
| 2 | 113 ÷ 24 = 4 remainder 17 |
| 3 | 24 ÷ 17 = 1 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 116 | 6612 |
| 78 and 39 | 78 |
| 63 and 22 | 1386 |
| 10 and 42 | 210 |
| 46 and 49 | 2254 |