Least Common Multiple (LCM) of 116 and 106
The least common multiple (LCM) of 116 and 106 is 6148.
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 116 and 106?
First, calculate the GCD of 116 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 106 = 1 remainder 10 |
| 2 | 106 ÷ 10 = 10 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 132 | 16764 |
| 38 and 75 | 2850 |
| 112 and 190 | 10640 |
| 36 and 54 | 108 |
| 79 and 100 | 7900 |