Least Common Multiple (LCM) of 113 and 100
The least common multiple (LCM) of 113 and 100 is 11300.
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 113 and 100?
First, calculate the GCD of 113 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 100 = 1 remainder 13 |
| 2 | 100 ÷ 13 = 7 remainder 9 |
| 3 | 13 ÷ 9 = 1 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 24 | 2280 |
| 84 and 187 | 15708 |
| 142 and 106 | 7526 |
| 138 and 48 | 1104 |
| 188 and 101 | 18988 |