Least Common Multiple (LCM) of 165 and 172
The least common multiple (LCM) of 165 and 172 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 165 and 172?
First, calculate the GCD of 165 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 172 = 0 remainder 165 |
| 2 | 172 ÷ 165 = 1 remainder 7 |
| 3 | 165 ÷ 7 = 23 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 25 | 3550 |
| 191 and 49 | 9359 |
| 137 and 76 | 10412 |
| 74 and 103 | 7622 |
| 30 and 80 | 240 |