Least Common Multiple (LCM) of 164 and 90
The least common multiple (LCM) of 164 and 90 is 7380.
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 164 and 90?
First, calculate the GCD of 164 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 90 = 1 remainder 74 |
| 2 | 90 ÷ 74 = 1 remainder 16 |
| 3 | 74 ÷ 16 = 4 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 150 | 4650 |
| 110 and 113 | 12430 |
| 180 and 100 | 900 |
| 190 and 63 | 11970 |
| 54 and 110 | 2970 |