Least Common Multiple (LCM) of 67 and 49
The least common multiple (LCM) of 67 and 49 is 3283.
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 67 and 49?
First, calculate the GCD of 67 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 49 = 1 remainder 18 |
| 2 | 49 ÷ 18 = 2 remainder 13 |
| 3 | 18 ÷ 13 = 1 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 15 | 285 |
| 57 and 130 | 7410 |
| 193 and 23 | 4439 |
| 18 and 54 | 54 |
| 68 and 125 | 8500 |