Least Common Multiple (LCM) of 96 and 113
The least common multiple (LCM) of 96 and 113 is 10848.
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 96 and 113?
First, calculate the GCD of 96 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 113 = 0 remainder 96 |
| 2 | 113 ÷ 96 = 1 remainder 17 |
| 3 | 96 ÷ 17 = 5 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 130 | 15990 |
| 164 and 17 | 2788 |
| 10 and 128 | 640 |
| 112 and 195 | 21840 |
| 45 and 157 | 7065 |