Least Common Multiple (LCM) of 172 and 45
The least common multiple (LCM) of 172 and 45 is 7740.
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 45?
First, calculate the GCD of 172 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 45 = 3 remainder 37 |
| 2 | 45 ÷ 37 = 1 remainder 8 |
| 3 | 37 ÷ 8 = 4 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 188 | 3196 |
| 39 and 21 | 273 |
| 164 and 41 | 164 |
| 46 and 129 | 5934 |
| 193 and 186 | 35898 |