Least Common Multiple (LCM) of 113 and 17
The least common multiple (LCM) of 113 and 17 is 1921.
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 17?
First, calculate the GCD of 113 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 17 = 6 remainder 11 |
| 2 | 17 ÷ 11 = 1 remainder 6 |
| 3 | 11 ÷ 6 = 1 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 149 | 11473 |
| 18 and 150 | 450 |
| 31 and 52 | 1612 |
| 116 and 35 | 4060 |
| 189 and 64 | 12096 |