Least Common Multiple (LCM) of 126 and 33
The least common multiple (LCM) of 126 and 33 is 1386.
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 126 and 33?
First, calculate the GCD of 126 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 33 = 3 remainder 27 |
| 2 | 33 ÷ 27 = 1 remainder 6 |
| 3 | 27 ÷ 6 = 4 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 32 | 1760 |
| 17 and 17 | 17 |
| 164 and 63 | 10332 |
| 186 and 153 | 9486 |
| 178 and 142 | 12638 |