Least Common Multiple (LCM) of 96 and 58
The least common multiple (LCM) of 96 and 58 is 2784.
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 58?
First, calculate the GCD of 96 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 58 = 1 remainder 38 |
| 2 | 58 ÷ 38 = 1 remainder 20 |
| 3 | 38 ÷ 20 = 1 remainder 18 |
| 4 | 20 ÷ 18 = 1 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 196 | 36260 |
| 34 and 160 | 2720 |
| 101 and 24 | 2424 |
| 116 and 184 | 5336 |
| 49 and 51 | 2499 |