Least Common Multiple (LCM) of 21 and 165
The least common multiple (LCM) of 21 and 165 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 21 and 165?
First, calculate the GCD of 21 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 165 = 0 remainder 21 |
| 2 | 165 ÷ 21 = 7 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 175 | 30800 |
| 30 and 64 | 960 |
| 40 and 105 | 840 |
| 188 and 129 | 24252 |
| 101 and 97 | 9797 |