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 |
|---|---|
| 17 and 133 | 2261 |
| 142 and 180 | 12780 |
| 166 and 83 | 166 |
| 191 and 172 | 32852 |
| 148 and 73 | 10804 |