Least Common Multiple (LCM) of 105 and 172
The least common multiple (LCM) of 105 and 172 is 18060.
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 172?
First, calculate the GCD of 105 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 172 = 0 remainder 105 |
| 2 | 172 ÷ 105 = 1 remainder 67 |
| 3 | 105 ÷ 67 = 1 remainder 38 |
| 4 | 67 ÷ 38 = 1 remainder 29 |
| 5 | 38 ÷ 29 = 1 remainder 9 |
| 6 | 29 ÷ 9 = 3 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 101 | 10302 |
| 71 and 115 | 8165 |
| 138 and 28 | 1932 |
| 171 and 45 | 855 |
| 48 and 131 | 6288 |