Least Common Multiple (LCM) of 113 and 117
The least common multiple (LCM) of 113 and 117 is 13221.
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 117?
First, calculate the GCD of 113 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 117 = 0 remainder 113 |
| 2 | 117 ÷ 113 = 1 remainder 4 |
| 3 | 113 ÷ 4 = 28 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 53 | 6890 |
| 39 and 108 | 1404 |
| 101 and 165 | 16665 |
| 42 and 135 | 1890 |
| 57 and 90 | 1710 |