Least Common Multiple (LCM) of 49 and 85
The least common multiple (LCM) of 49 and 85 is 4165.
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 49 and 85?
First, calculate the GCD of 49 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 85 = 0 remainder 49 |
| 2 | 85 ÷ 49 = 1 remainder 36 |
| 3 | 49 ÷ 36 = 1 remainder 13 |
| 4 | 36 ÷ 13 = 2 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 84 | 2184 |
| 65 and 81 | 5265 |
| 105 and 144 | 5040 |
| 81 and 66 | 1782 |
| 97 and 156 | 15132 |