Least Common Multiple (LCM) of 113 and 106
The least common multiple (LCM) of 113 and 106 is 11978.
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 106?
First, calculate the GCD of 113 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 106 = 1 remainder 7 |
| 2 | 106 ÷ 7 = 15 remainder 1 |
| 3 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 78 | 1950 |
| 125 and 19 | 2375 |
| 115 and 66 | 7590 |
| 106 and 195 | 20670 |
| 52 and 108 | 1404 |