Least Common Multiple (LCM) of 33 and 106
The least common multiple (LCM) of 33 and 106 is 3498.
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 106?
First, calculate the GCD of 33 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 106 = 0 remainder 33 |
| 2 | 106 ÷ 33 = 3 remainder 7 |
| 3 | 33 ÷ 7 = 4 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 184 | 20424 |
| 86 and 72 | 3096 |
| 196 and 166 | 16268 |
| 167 and 99 | 16533 |
| 48 and 174 | 1392 |