Least Common Multiple (LCM) of 49 and 53
The least common multiple (LCM) of 49 and 53 is 2597.
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 53?
First, calculate the GCD of 49 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 53 = 0 remainder 49 |
| 2 | 53 ÷ 49 = 1 remainder 4 |
| 3 | 49 ÷ 4 = 12 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 74 | 3108 |
| 185 and 96 | 17760 |
| 162 and 129 | 6966 |
| 139 and 137 | 19043 |
| 21 and 57 | 399 |