Least Common Multiple (LCM) of 33 and 60
The least common multiple (LCM) of 33 and 60 is 660.
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 60?
First, calculate the GCD of 33 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 60 = 0 remainder 33 |
| 2 | 60 ÷ 33 = 1 remainder 27 |
| 3 | 33 ÷ 27 = 1 remainder 6 |
| 4 | 27 ÷ 6 = 4 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 159 | 20352 |
| 196 and 72 | 3528 |
| 139 and 76 | 10564 |
| 113 and 52 | 5876 |
| 112 and 25 | 2800 |