Least Common Multiple (LCM) of 190 and 99
The least common multiple (LCM) of 190 and 99 is 18810.
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 190 and 99?
First, calculate the GCD of 190 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 99 = 1 remainder 91 |
| 2 | 99 ÷ 91 = 1 remainder 8 |
| 3 | 91 ÷ 8 = 11 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 132 | 924 |
| 16 and 69 | 1104 |
| 156 and 102 | 2652 |
| 114 and 123 | 4674 |
| 78 and 143 | 858 |