Least Common Multiple (LCM) of 90 and 113
The least common multiple (LCM) of 90 and 113 is 10170.
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 113?
First, calculate the GCD of 90 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 113 = 0 remainder 90 |
| 2 | 113 ÷ 90 = 1 remainder 23 |
| 3 | 90 ÷ 23 = 3 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 82 | 4592 |
| 106 and 13 | 1378 |
| 12 and 40 | 120 |
| 179 and 128 | 22912 |
| 125 and 133 | 16625 |