Least Common Multiple (LCM) of 20 and 113
The least common multiple (LCM) of 20 and 113 is 2260.
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 20 and 113?
First, calculate the GCD of 20 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 113 = 0 remainder 20 |
| 2 | 113 ÷ 20 = 5 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 187 | 34221 |
| 22 and 152 | 1672 |
| 107 and 174 | 18618 |
| 158 and 130 | 10270 |
| 71 and 145 | 10295 |