Least Common Multiple (LCM) of 90 and 38
The least common multiple (LCM) of 90 and 38 is 1710.
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 90 and 38?
First, calculate the GCD of 90 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 38 = 2 remainder 14 |
| 2 | 38 ÷ 14 = 2 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 95 | 6365 |
| 95 and 94 | 8930 |
| 165 and 21 | 1155 |
| 105 and 149 | 15645 |
| 173 and 42 | 7266 |