Least Common Multiple (LCM) of 49 and 67
The least common multiple (LCM) of 49 and 67 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 49 and 67?
First, calculate the GCD of 49 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 67 = 0 remainder 49 |
| 2 | 67 ÷ 49 = 1 remainder 18 |
| 3 | 49 ÷ 18 = 2 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 137 | 18221 |
| 130 and 122 | 7930 |
| 26 and 155 | 4030 |
| 144 and 15 | 720 |
| 146 and 81 | 11826 |