Least Common Multiple (LCM) of 99 and 53
The least common multiple (LCM) of 99 and 53 is 5247.
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 99 and 53?
First, calculate the GCD of 99 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 53 = 1 remainder 46 |
| 2 | 53 ÷ 46 = 1 remainder 7 |
| 3 | 46 ÷ 7 = 6 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 169 | 28392 |
| 67 and 106 | 7102 |
| 160 and 74 | 5920 |
| 35 and 183 | 6405 |
| 126 and 97 | 12222 |