Least Common Multiple (LCM) of 58 and 96
The least common multiple (LCM) of 58 and 96 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 58 and 96?
First, calculate the GCD of 58 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 96 = 0 remainder 58 |
| 2 | 96 ÷ 58 = 1 remainder 38 |
| 3 | 58 ÷ 38 = 1 remainder 20 |
| 4 | 38 ÷ 20 = 1 remainder 18 |
| 5 | 20 ÷ 18 = 1 remainder 2 |
| 6 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 126 | 1386 |
| 155 and 79 | 12245 |
| 28 and 59 | 1652 |
| 21 and 15 | 105 |
| 134 and 169 | 22646 |