Least Common Multiple (LCM) of 61 and 105
The least common multiple (LCM) of 61 and 105 is 6405.
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 61 and 105?
First, calculate the GCD of 61 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 105 = 0 remainder 61 |
| 2 | 105 ÷ 61 = 1 remainder 44 |
| 3 | 61 ÷ 44 = 1 remainder 17 |
| 4 | 44 ÷ 17 = 2 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 29 | 4785 |
| 113 and 22 | 2486 |
| 178 and 169 | 30082 |
| 18 and 159 | 954 |
| 92 and 74 | 3404 |