Least Common Multiple (LCM) of 90 and 52
The least common multiple (LCM) of 90 and 52 is 2340.
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 52?
First, calculate the GCD of 90 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 52 = 1 remainder 38 |
| 2 | 52 ÷ 38 = 1 remainder 14 |
| 3 | 38 ÷ 14 = 2 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 118 | 6490 |
| 139 and 193 | 26827 |
| 31 and 119 | 3689 |
| 85 and 105 | 1785 |
| 14 and 78 | 546 |