Least Common Multiple (LCM) of 49 and 84
The least common multiple (LCM) of 49 and 84 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 49 and 84?
First, calculate the GCD of 49 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 84 = 0 remainder 49 |
| 2 | 84 ÷ 49 = 1 remainder 35 |
| 3 | 49 ÷ 35 = 1 remainder 14 |
| 4 | 35 ÷ 14 = 2 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 144 | 1008 |
| 82 and 91 | 7462 |
| 197 and 28 | 5516 |
| 135 and 71 | 9585 |
| 46 and 107 | 4922 |