Least Common Multiple (LCM) of 168 and 103
The least common multiple (LCM) of 168 and 103 is 17304.
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 103?
First, calculate the GCD of 168 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 103 = 1 remainder 65 |
| 2 | 103 ÷ 65 = 1 remainder 38 |
| 3 | 65 ÷ 38 = 1 remainder 27 |
| 4 | 38 ÷ 27 = 1 remainder 11 |
| 5 | 27 ÷ 11 = 2 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 191 | 20055 |
| 83 and 170 | 14110 |
| 21 and 192 | 1344 |
| 31 and 124 | 124 |
| 192 and 66 | 2112 |