Least Common Multiple (LCM) of 105 and 168
The least common multiple (LCM) of 105 and 168 is 840.
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 168?
First, calculate the GCD of 105 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 168 = 0 remainder 105 |
| 2 | 168 ÷ 105 = 1 remainder 63 |
| 3 | 105 ÷ 63 = 1 remainder 42 |
| 4 | 63 ÷ 42 = 1 remainder 21 |
| 5 | 42 ÷ 21 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 96 | 1248 |
| 31 and 113 | 3503 |
| 177 and 29 | 5133 |
| 125 and 19 | 2375 |
| 97 and 172 | 16684 |