Least Common Multiple (LCM) of 90 and 133
The least common multiple (LCM) of 90 and 133 is 11970.
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 133?
First, calculate the GCD of 90 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 133 = 0 remainder 90 |
| 2 | 133 ÷ 90 = 1 remainder 43 |
| 3 | 90 ÷ 43 = 2 remainder 4 |
| 4 | 43 ÷ 4 = 10 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 122 | 7076 |
| 176 and 72 | 1584 |
| 175 and 135 | 4725 |
| 131 and 42 | 5502 |
| 111 and 32 | 3552 |