Least Common Multiple (LCM) of 113 and 66
The least common multiple (LCM) of 113 and 66 is 7458.
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 113 and 66?
First, calculate the GCD of 113 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 66 = 1 remainder 47 |
| 2 | 66 ÷ 47 = 1 remainder 19 |
| 3 | 47 ÷ 19 = 2 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 123 | 17097 |
| 182 and 53 | 9646 |
| 22 and 24 | 264 |
| 30 and 87 | 870 |
| 72 and 133 | 9576 |