Least Common Multiple (LCM) of 90 and 111
The least common multiple (LCM) of 90 and 111 is 3330.
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 111?
First, calculate the GCD of 90 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 111 = 0 remainder 90 |
| 2 | 111 ÷ 90 = 1 remainder 21 |
| 3 | 90 ÷ 21 = 4 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 86 | 10062 |
| 114 and 59 | 6726 |
| 47 and 71 | 3337 |
| 155 and 132 | 20460 |
| 58 and 181 | 10498 |