Least Common Multiple (LCM) of 105 and 61
The least common multiple (LCM) of 105 and 61 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 105 and 61?
First, calculate the GCD of 105 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 61 = 1 remainder 44 |
| 2 | 61 ÷ 44 = 1 remainder 17 |
| 3 | 44 ÷ 17 = 2 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 144 | 3312 |
| 100 and 19 | 1900 |
| 38 and 164 | 3116 |
| 46 and 142 | 3266 |
| 117 and 22 | 2574 |