Least Common Multiple (LCM) of 99 and 52
The least common multiple (LCM) of 99 and 52 is 5148.
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 52?
First, calculate the GCD of 99 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 52 = 1 remainder 47 |
| 2 | 52 ÷ 47 = 1 remainder 5 |
| 3 | 47 ÷ 5 = 9 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 121 | 1936 |
| 59 and 64 | 3776 |
| 152 and 137 | 20824 |
| 31 and 95 | 2945 |
| 199 and 68 | 13532 |