Least Common Multiple (LCM) of 58 and 99
The least common multiple (LCM) of 58 and 99 is 5742.
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 99?
First, calculate the GCD of 58 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 99 = 0 remainder 58 |
| 2 | 99 ÷ 58 = 1 remainder 41 |
| 3 | 58 ÷ 41 = 1 remainder 17 |
| 4 | 41 ÷ 17 = 2 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 22 | 1100 |
| 33 and 144 | 1584 |
| 110 and 173 | 19030 |
| 123 and 106 | 13038 |
| 15 and 119 | 1785 |