Least Common Multiple (LCM) of 99 and 130
The least common multiple (LCM) of 99 and 130 is 12870.
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 130?
First, calculate the GCD of 99 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 130 = 0 remainder 99 |
| 2 | 130 ÷ 99 = 1 remainder 31 |
| 3 | 99 ÷ 31 = 3 remainder 6 |
| 4 | 31 ÷ 6 = 5 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 27 | 351 |
| 96 and 31 | 2976 |
| 149 and 129 | 19221 |
| 107 and 29 | 3103 |
| 174 and 120 | 3480 |