Least Common Multiple (LCM) of 105 and 169
The least common multiple (LCM) of 105 and 169 is 17745.
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 105 and 169?
First, calculate the GCD of 105 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 169 = 0 remainder 105 |
| 2 | 169 ÷ 105 = 1 remainder 64 |
| 3 | 105 ÷ 64 = 1 remainder 41 |
| 4 | 64 ÷ 41 = 1 remainder 23 |
| 5 | 41 ÷ 23 = 1 remainder 18 |
| 6 | 23 ÷ 18 = 1 remainder 5 |
| 7 | 18 ÷ 5 = 3 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 |
|---|---|
| 135 and 86 | 11610 |
| 126 and 148 | 9324 |
| 75 and 184 | 13800 |
| 85 and 43 | 3655 |
| 105 and 106 | 11130 |