Least Common Multiple (LCM) of 168 and 104
The least common multiple (LCM) of 168 and 104 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 168 and 104?
First, calculate the GCD of 168 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 104 = 1 remainder 64 |
| 2 | 104 ÷ 64 = 1 remainder 40 |
| 3 | 64 ÷ 40 = 1 remainder 24 |
| 4 | 40 ÷ 24 = 1 remainder 16 |
| 5 | 24 ÷ 16 = 1 remainder 8 |
| 6 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 49 | 4410 |
| 198 and 37 | 7326 |
| 51 and 158 | 8058 |
| 189 and 171 | 3591 |
| 58 and 141 | 8178 |