Least Common Multiple (LCM) of 111 and 33
The least common multiple (LCM) of 111 and 33 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 111 and 33?
First, calculate the GCD of 111 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 33 = 3 remainder 12 |
| 2 | 33 ÷ 12 = 2 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 170 | 17510 |
| 124 and 32 | 992 |
| 33 and 178 | 5874 |
| 126 and 89 | 11214 |
| 14 and 43 | 602 |