Least Common Multiple (LCM) of 52 and 85
The least common multiple (LCM) of 52 and 85 is 4420.
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 52 and 85?
First, calculate the GCD of 52 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 85 = 0 remainder 52 |
| 2 | 85 ÷ 52 = 1 remainder 33 |
| 3 | 52 ÷ 33 = 1 remainder 19 |
| 4 | 33 ÷ 19 = 1 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 10 | 120 |
| 38 and 191 | 7258 |
| 168 and 77 | 1848 |
| 150 and 72 | 1800 |
| 135 and 22 | 2970 |