Least Common Multiple (LCM) of 58 and 100
The least common multiple (LCM) of 58 and 100 is 2900.
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 100?
First, calculate the GCD of 58 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 100 = 0 remainder 58 |
| 2 | 100 ÷ 58 = 1 remainder 42 |
| 3 | 58 ÷ 42 = 1 remainder 16 |
| 4 | 42 ÷ 16 = 2 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 101 | 14241 |
| 143 and 88 | 1144 |
| 91 and 115 | 10465 |
| 83 and 185 | 15355 |
| 197 and 98 | 19306 |