Least Common Multiple (LCM) of 33 and 97
The least common multiple (LCM) of 33 and 97 is 3201.
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 97?
First, calculate the GCD of 33 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 97 = 0 remainder 33 |
| 2 | 97 ÷ 33 = 2 remainder 31 |
| 3 | 33 ÷ 31 = 1 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 35 | 3535 |
| 101 and 26 | 2626 |
| 102 and 139 | 14178 |
| 153 and 148 | 22644 |
| 37 and 90 | 3330 |