Least Common Multiple (LCM) of 90 and 146
The least common multiple (LCM) of 90 and 146 is 6570.
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 146?
First, calculate the GCD of 90 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 146 = 0 remainder 90 |
| 2 | 146 ÷ 90 = 1 remainder 56 |
| 3 | 90 ÷ 56 = 1 remainder 34 |
| 4 | 56 ÷ 34 = 1 remainder 22 |
| 5 | 34 ÷ 22 = 1 remainder 12 |
| 6 | 22 ÷ 12 = 1 remainder 10 |
| 7 | 12 ÷ 10 = 1 remainder 2 |
| 8 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 169 | 21801 |
| 43 and 169 | 7267 |
| 113 and 49 | 5537 |
| 89 and 99 | 8811 |
| 165 and 12 | 660 |