Least Common Multiple (LCM) of 113 and 11
The least common multiple (LCM) of 113 and 11 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 113 and 11?
First, calculate the GCD of 113 and 11 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 11 = 10 remainder 3 |
| 2 | 11 ÷ 3 = 3 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 42 | 5334 |
| 174 and 160 | 13920 |
| 108 and 30 | 540 |
| 190 and 78 | 7410 |
| 188 and 133 | 25004 |