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 |
|---|---|
| 141 and 46 | 6486 |
| 76 and 135 | 10260 |
| 31 and 136 | 4216 |
| 173 and 16 | 2768 |
| 117 and 151 | 17667 |