Least Common Multiple (LCM) of 106 and 61
The least common multiple (LCM) of 106 and 61 is 6466.
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 106 and 61?
First, calculate the GCD of 106 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 61 = 1 remainder 45 |
| 2 | 61 ÷ 45 = 1 remainder 16 |
| 3 | 45 ÷ 16 = 2 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 81 | 4536 |
| 105 and 149 | 15645 |
| 54 and 70 | 1890 |
| 172 and 14 | 1204 |
| 115 and 192 | 22080 |