Least Common Multiple (LCM) of 109 and 90
The least common multiple (LCM) of 109 and 90 is 9810.
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 109 and 90?
First, calculate the GCD of 109 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 90 = 1 remainder 19 |
| 2 | 90 ÷ 19 = 4 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 39 | 6825 |
| 22 and 156 | 1716 |
| 99 and 173 | 17127 |
| 64 and 190 | 6080 |
| 77 and 20 | 1540 |