Least Common Multiple (LCM) of 21 and 33
The least common multiple (LCM) of 21 and 33 is 231.
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 33?
First, calculate the GCD of 21 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 33 = 0 remainder 21 |
| 2 | 33 ÷ 21 = 1 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 18 | 3114 |
| 41 and 50 | 2050 |
| 32 and 16 | 32 |
| 172 and 87 | 14964 |
| 118 and 95 | 11210 |