Least Common Multiple (LCM) of 165 and 21
The least common multiple (LCM) of 165 and 21 is 1155.
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 21?
First, calculate the GCD of 165 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 21 = 7 remainder 18 |
| 2 | 21 ÷ 18 = 1 remainder 3 |
| 3 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 23 | 3450 |
| 27 and 30 | 270 |
| 103 and 141 | 14523 |
| 187 and 105 | 19635 |
| 89 and 167 | 14863 |