Least Common Multiple (LCM) of 16 and 107
The least common multiple (LCM) of 16 and 107 is 1712.
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 107?
First, calculate the GCD of 16 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 107 = 0 remainder 16 |
| 2 | 107 ÷ 16 = 6 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 49 | 5782 |
| 175 and 142 | 24850 |
| 146 and 160 | 11680 |
| 146 and 161 | 23506 |
| 10 and 133 | 1330 |