Least Common Multiple (LCM) of 52 and 90
The least common multiple (LCM) of 52 and 90 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 52 and 90?
First, calculate the GCD of 52 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 90 = 0 remainder 52 |
| 2 | 90 ÷ 52 = 1 remainder 38 |
| 3 | 52 ÷ 38 = 1 remainder 14 |
| 4 | 38 ÷ 14 = 2 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 104 | 936 |
| 197 and 13 | 2561 |
| 173 and 170 | 29410 |
| 129 and 96 | 4128 |
| 12 and 33 | 132 |