Least Common Multiple (LCM) of 90 and 53
The least common multiple (LCM) of 90 and 53 is 4770.
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 53?
First, calculate the GCD of 90 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 53 = 1 remainder 37 |
| 2 | 53 ÷ 37 = 1 remainder 16 |
| 3 | 37 ÷ 16 = 2 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 189 | 3780 |
| 37 and 177 | 6549 |
| 147 and 104 | 15288 |
| 135 and 25 | 675 |
| 127 and 97 | 12319 |