Least Common Multiple (LCM) of 84 and 165
The least common multiple (LCM) of 84 and 165 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 84 and 165?
First, calculate the GCD of 84 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 165 = 0 remainder 84 |
| 2 | 165 ÷ 84 = 1 remainder 81 |
| 3 | 84 ÷ 81 = 1 remainder 3 |
| 4 | 81 ÷ 3 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 27 | 4509 |
| 185 and 166 | 30710 |
| 151 and 113 | 17063 |
| 81 and 194 | 15714 |
| 105 and 64 | 6720 |