Least Common Multiple (LCM) of 34 and 88
The least common multiple (LCM) of 34 and 88 is 1496.
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 88?
First, calculate the GCD of 34 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 88 = 0 remainder 34 |
| 2 | 88 ÷ 34 = 2 remainder 20 |
| 3 | 34 ÷ 20 = 1 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 153 | 16677 |
| 99 and 84 | 2772 |
| 84 and 200 | 4200 |
| 109 and 195 | 21255 |
| 46 and 77 | 3542 |