Least Common Multiple (LCM) of 172 and 165
The least common multiple (LCM) of 172 and 165 is 28380.
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 165?
First, calculate the GCD of 172 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 165 = 1 remainder 7 |
| 2 | 165 ÷ 7 = 23 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 37 | 74 |
| 159 and 76 | 12084 |
| 47 and 162 | 7614 |
| 105 and 152 | 15960 |
| 85 and 128 | 10880 |