Least Common Multiple (LCM) of 99 and 38
The least common multiple (LCM) of 99 and 38 is 3762.
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 38?
First, calculate the GCD of 99 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 38 = 2 remainder 23 |
| 2 | 38 ÷ 23 = 1 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 194 | 21922 |
| 196 and 193 | 37828 |
| 67 and 126 | 8442 |
| 73 and 56 | 4088 |
| 45 and 72 | 360 |