Least Common Multiple (LCM) of 103 and 169
The least common multiple (LCM) of 103 and 169 is 17407.
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 169?
First, calculate the GCD of 103 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 169 = 0 remainder 103 |
| 2 | 169 ÷ 103 = 1 remainder 66 |
| 3 | 103 ÷ 66 = 1 remainder 37 |
| 4 | 66 ÷ 37 = 1 remainder 29 |
| 5 | 37 ÷ 29 = 1 remainder 8 |
| 6 | 29 ÷ 8 = 3 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 195 | 195 |
| 153 and 27 | 459 |
| 156 and 42 | 1092 |
| 72 and 148 | 2664 |
| 104 and 189 | 19656 |