Least Common Multiple (LCM) of 12 and 49
The least common multiple (LCM) of 12 and 49 is 588.
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 12 and 49?
First, calculate the GCD of 12 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 49 = 0 remainder 12 |
| 2 | 49 ÷ 12 = 4 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 48 | 1968 |
| 189 and 135 | 945 |
| 133 and 87 | 11571 |
| 192 and 102 | 3264 |
| 103 and 17 | 1751 |