Least Common Multiple (LCM) of 105 and 14
The least common multiple (LCM) of 105 and 14 is 210.
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 105 and 14?
First, calculate the GCD of 105 and 14 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 14 = 7 remainder 7 |
| 2 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 113 | 3842 |
| 177 and 114 | 6726 |
| 17 and 38 | 646 |
| 125 and 195 | 4875 |
| 121 and 24 | 2904 |