Least Common Multiple (LCM) of 90 and 161
The least common multiple (LCM) of 90 and 161 is 14490.
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 161?
First, calculate the GCD of 90 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 161 = 0 remainder 90 |
| 2 | 161 ÷ 90 = 1 remainder 71 |
| 3 | 90 ÷ 71 = 1 remainder 19 |
| 4 | 71 ÷ 19 = 3 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 119 | 119 |
| 54 and 134 | 3618 |
| 165 and 164 | 27060 |
| 90 and 109 | 9810 |
| 193 and 174 | 33582 |