Least Common Multiple (LCM) of 33 and 78
The least common multiple (LCM) of 33 and 78 is 858.
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 78?
First, calculate the GCD of 33 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 78 = 0 remainder 33 |
| 2 | 78 ÷ 33 = 2 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 132 | 6468 |
| 123 and 199 | 24477 |
| 79 and 124 | 9796 |
| 110 and 60 | 660 |
| 81 and 63 | 567 |