Least Common Multiple (LCM) of 105 and 13
The least common multiple (LCM) of 105 and 13 is 1365.
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 13?
First, calculate the GCD of 105 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 13 = 8 remainder 1 |
| 2 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 187 | 1309 |
| 109 and 161 | 17549 |
| 43 and 77 | 3311 |
| 122 and 156 | 9516 |
| 70 and 111 | 7770 |