Least Common Multiple (LCM) of 103 and 168
The least common multiple (LCM) of 103 and 168 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 103 and 168?
First, calculate the GCD of 103 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 168 = 0 remainder 103 |
| 2 | 168 ÷ 103 = 1 remainder 65 |
| 3 | 103 ÷ 65 = 1 remainder 38 |
| 4 | 65 ÷ 38 = 1 remainder 27 |
| 5 | 38 ÷ 27 = 1 remainder 11 |
| 6 | 27 ÷ 11 = 2 remainder 5 |
| 7 | 11 ÷ 5 = 2 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 117 | 468 |
| 118 and 138 | 8142 |
| 138 and 58 | 4002 |
| 41 and 162 | 6642 |
| 95 and 80 | 1520 |