Least Common Multiple (LCM) of 33 and 178
The least common multiple (LCM) of 33 and 178 is 5874.
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 178?
First, calculate the GCD of 33 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 178 = 0 remainder 33 |
| 2 | 178 ÷ 33 = 5 remainder 13 |
| 3 | 33 ÷ 13 = 2 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 138 | 12972 |
| 75 and 22 | 1650 |
| 83 and 114 | 9462 |
| 48 and 17 | 816 |
| 134 and 109 | 14606 |