Least Common Multiple (LCM) of 34 and 52
The least common multiple (LCM) of 34 and 52 is 884.
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 52?
First, calculate the GCD of 34 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 52 = 0 remainder 34 |
| 2 | 52 ÷ 34 = 1 remainder 18 |
| 3 | 34 ÷ 18 = 1 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 168 | 1176 |
| 194 and 14 | 1358 |
| 172 and 119 | 20468 |
| 69 and 130 | 8970 |
| 96 and 182 | 8736 |