Least Common Multiple (LCM) of 11 and 113
The least common multiple (LCM) of 11 and 113 is 1243.
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 11 and 113?
First, calculate the GCD of 11 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 113 = 0 remainder 11 |
| 2 | 113 ÷ 11 = 10 remainder 3 |
| 3 | 11 ÷ 3 = 3 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 162 | 19278 |
| 37 and 162 | 5994 |
| 77 and 19 | 1463 |
| 104 and 145 | 15080 |
| 175 and 39 | 6825 |