Least Common Multiple (LCM) of 113 and 156
The least common multiple (LCM) of 113 and 156 is 17628.
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 156?
First, calculate the GCD of 113 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 156 = 0 remainder 113 |
| 2 | 156 ÷ 113 = 1 remainder 43 |
| 3 | 113 ÷ 43 = 2 remainder 27 |
| 4 | 43 ÷ 27 = 1 remainder 16 |
| 5 | 27 ÷ 16 = 1 remainder 11 |
| 6 | 16 ÷ 11 = 1 remainder 5 |
| 7 | 11 ÷ 5 = 2 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 105 | 2730 |
| 155 and 21 | 3255 |
| 193 and 17 | 3281 |
| 49 and 199 | 9751 |
| 54 and 97 | 5238 |