Least Common Multiple (LCM) of 16 and 106
The least common multiple (LCM) of 16 and 106 is 848.
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 16 and 106?
First, calculate the GCD of 16 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 106 = 0 remainder 16 |
| 2 | 106 ÷ 16 = 6 remainder 10 |
| 3 | 16 ÷ 10 = 1 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 119 | 12376 |
| 182 and 157 | 28574 |
| 30 and 41 | 1230 |
| 88 and 91 | 8008 |
| 139 and 168 | 23352 |