Least Common Multiple (LCM) of 109 and 16
The least common multiple (LCM) of 109 and 16 is 1744.
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 109 and 16?
First, calculate the GCD of 109 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 16 = 6 remainder 13 |
| 2 | 16 ÷ 13 = 1 remainder 3 |
| 3 | 13 ÷ 3 = 4 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 59 | 8024 |
| 74 and 27 | 1998 |
| 68 and 66 | 2244 |
| 75 and 31 | 2325 |
| 71 and 118 | 8378 |