Least Common Multiple (LCM) of 114 and 33
The least common multiple (LCM) of 114 and 33 is 1254.
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 114 and 33?
First, calculate the GCD of 114 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 33 = 3 remainder 15 |
| 2 | 33 ÷ 15 = 2 remainder 3 |
| 3 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 106 | 13674 |
| 106 and 77 | 8162 |
| 188 and 32 | 1504 |
| 176 and 19 | 3344 |
| 189 and 82 | 15498 |