Least Common Multiple (LCM) of 49 and 32
The least common multiple (LCM) of 49 and 32 is 1568.
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 32?
First, calculate the GCD of 49 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 32 = 1 remainder 17 |
| 2 | 32 ÷ 17 = 1 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 131 | 23842 |
| 168 and 187 | 31416 |
| 199 and 94 | 18706 |
| 23 and 71 | 1633 |
| 120 and 195 | 1560 |