Least Common Multiple (LCM) of 34 and 84
The least common multiple (LCM) of 34 and 84 is 1428.
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 84?
First, calculate the GCD of 34 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 84 = 0 remainder 34 |
| 2 | 84 ÷ 34 = 2 remainder 16 |
| 3 | 34 ÷ 16 = 2 remainder 2 |
| 4 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 61 | 8601 |
| 42 and 66 | 462 |
| 145 and 82 | 11890 |
| 96 and 54 | 864 |
| 16 and 123 | 1968 |