Least Common Multiple (LCM) of 90 and 170
The least common multiple (LCM) of 90 and 170 is 1530.
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 170?
First, calculate the GCD of 90 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 170 = 0 remainder 90 |
| 2 | 170 ÷ 90 = 1 remainder 80 |
| 3 | 90 ÷ 80 = 1 remainder 10 |
| 4 | 80 ÷ 10 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 98 | 12642 |
| 72 and 54 | 216 |
| 130 and 15 | 390 |
| 12 and 90 | 180 |
| 104 and 90 | 4680 |