Least Common Multiple (LCM) of 33 and 111
The least common multiple (LCM) of 33 and 111 is 1221.
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 33 and 111?
First, calculate the GCD of 33 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 111 = 0 remainder 33 |
| 2 | 111 ÷ 33 = 3 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 126 | 21294 |
| 54 and 36 | 108 |
| 97 and 184 | 17848 |
| 132 and 129 | 5676 |
| 131 and 43 | 5633 |