Least Common Multiple (LCM) of 105 and 39
The least common multiple (LCM) of 105 and 39 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 39?
First, calculate the GCD of 105 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 39 = 2 remainder 27 |
| 2 | 39 ÷ 27 = 1 remainder 12 |
| 3 | 27 ÷ 12 = 2 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 174 | 870 |
| 115 and 118 | 13570 |
| 172 and 59 | 10148 |
| 98 and 44 | 2156 |
| 164 and 75 | 12300 |