Least Common Multiple (LCM) of 90 and 166
The least common multiple (LCM) of 90 and 166 is 7470.
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 166?
First, calculate the GCD of 90 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 166 = 0 remainder 90 |
| 2 | 166 ÷ 90 = 1 remainder 76 |
| 3 | 90 ÷ 76 = 1 remainder 14 |
| 4 | 76 ÷ 14 = 5 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 42 | 1554 |
| 21 and 31 | 651 |
| 187 and 33 | 561 |
| 103 and 116 | 11948 |
| 20 and 41 | 820 |