Least Common Multiple (LCM) of 33 and 90
The least common multiple (LCM) of 33 and 90 is 990.
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 90?
First, calculate the GCD of 33 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 90 = 0 remainder 33 |
| 2 | 90 ÷ 33 = 2 remainder 24 |
| 3 | 33 ÷ 24 = 1 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 53 | 9434 |
| 123 and 87 | 3567 |
| 75 and 44 | 3300 |
| 53 and 65 | 3445 |
| 140 and 200 | 1400 |