Least Common Multiple (LCM) of 113 and 142
The least common multiple (LCM) of 113 and 142 is 16046.
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 142?
First, calculate the GCD of 113 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 142 = 0 remainder 113 |
| 2 | 142 ÷ 113 = 1 remainder 29 |
| 3 | 113 ÷ 29 = 3 remainder 26 |
| 4 | 29 ÷ 26 = 1 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 169 | 7098 |
| 101 and 46 | 4646 |
| 80 and 63 | 5040 |
| 173 and 175 | 30275 |
| 22 and 37 | 814 |