Least Common Multiple (LCM) of 34 and 96
The least common multiple (LCM) of 34 and 96 is 1632.
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 34 and 96?
First, calculate the GCD of 34 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 96 = 0 remainder 34 |
| 2 | 96 ÷ 34 = 2 remainder 28 |
| 3 | 34 ÷ 28 = 1 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 164 | 17548 |
| 91 and 133 | 1729 |
| 200 and 55 | 2200 |
| 132 and 55 | 660 |
| 185 and 145 | 5365 |