Least Common Multiple (LCM) of 165 and 84
The least common multiple (LCM) of 165 and 84 is 4620.
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 84?
First, calculate the GCD of 165 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 84 = 1 remainder 81 |
| 2 | 84 ÷ 81 = 1 remainder 3 |
| 3 | 81 ÷ 3 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 38 | 1976 |
| 105 and 70 | 210 |
| 34 and 103 | 3502 |
| 103 and 41 | 4223 |
| 162 and 160 | 12960 |