Least Common Multiple (LCM) of 171 and 105
The least common multiple (LCM) of 171 and 105 is 5985.
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 171 and 105?
First, calculate the GCD of 171 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 105 = 1 remainder 66 |
| 2 | 105 ÷ 66 = 1 remainder 39 |
| 3 | 66 ÷ 39 = 1 remainder 27 |
| 4 | 39 ÷ 27 = 1 remainder 12 |
| 5 | 27 ÷ 12 = 2 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 146 | 1314 |
| 138 and 118 | 8142 |
| 106 and 112 | 5936 |
| 73 and 53 | 3869 |
| 109 and 21 | 2289 |