Least Common Multiple (LCM) of 33 and 138
The least common multiple (LCM) of 33 and 138 is 1518.
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 138?
First, calculate the GCD of 33 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 138 = 0 remainder 33 |
| 2 | 138 ÷ 33 = 4 remainder 6 |
| 3 | 33 ÷ 6 = 5 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 104 | 1456 |
| 102 and 72 | 1224 |
| 49 and 101 | 4949 |
| 72 and 171 | 1368 |
| 94 and 45 | 4230 |