Least Common Multiple (LCM) of 38 and 165
The least common multiple (LCM) of 38 and 165 is 6270.
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 38 and 165?
First, calculate the GCD of 38 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 165 = 0 remainder 38 |
| 2 | 165 ÷ 38 = 4 remainder 13 |
| 3 | 38 ÷ 13 = 2 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 74 | 11618 |
| 14 and 41 | 574 |
| 161 and 36 | 5796 |
| 109 and 176 | 19184 |
| 88 and 161 | 14168 |