Least Common Multiple (LCM) of 172 and 105
The least common multiple (LCM) of 172 and 105 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 172 and 105?
First, calculate the GCD of 172 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 105 = 1 remainder 67 |
| 2 | 105 ÷ 67 = 1 remainder 38 |
| 3 | 67 ÷ 38 = 1 remainder 29 |
| 4 | 38 ÷ 29 = 1 remainder 9 |
| 5 | 29 ÷ 9 = 3 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 77 | 7854 |
| 60 and 68 | 1020 |
| 127 and 97 | 12319 |
| 32 and 133 | 4256 |
| 77 and 93 | 7161 |