Least Common Multiple (LCM) of 90 and 28
The least common multiple (LCM) of 90 and 28 is 1260.
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 28?
First, calculate the GCD of 90 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 28 = 3 remainder 6 |
| 2 | 28 ÷ 6 = 4 remainder 4 |
| 3 | 6 ÷ 4 = 1 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 79 | 10112 |
| 75 and 195 | 975 |
| 123 and 129 | 5289 |
| 35 and 29 | 1015 |
| 80 and 14 | 560 |