Least Common Multiple (LCM) of 104 and 168
The least common multiple (LCM) of 104 and 168 is 2184.
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 104 and 168?
First, calculate the GCD of 104 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 168 = 0 remainder 104 |
| 2 | 168 ÷ 104 = 1 remainder 64 |
| 3 | 104 ÷ 64 = 1 remainder 40 |
| 4 | 64 ÷ 40 = 1 remainder 24 |
| 5 | 40 ÷ 24 = 1 remainder 16 |
| 6 | 24 ÷ 16 = 1 remainder 8 |
| 7 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 112 | 560 |
| 82 and 84 | 3444 |
| 145 and 41 | 5945 |
| 31 and 147 | 4557 |
| 134 and 40 | 2680 |