Least Common Multiple (LCM) of 53 and 99
The least common multiple (LCM) of 53 and 99 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 53 and 99?
First, calculate the GCD of 53 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 99 = 0 remainder 53 |
| 2 | 99 ÷ 53 = 1 remainder 46 |
| 3 | 53 ÷ 46 = 1 remainder 7 |
| 4 | 46 ÷ 7 = 6 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 181 | 12670 |
| 77 and 38 | 2926 |
| 123 and 80 | 9840 |
| 10 and 23 | 230 |
| 63 and 126 | 126 |