Least Common Multiple (LCM) of 142 and 113
The least common multiple (LCM) of 142 and 113 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 142 and 113?
First, calculate the GCD of 142 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 113 = 1 remainder 29 |
| 2 | 113 ÷ 29 = 3 remainder 26 |
| 3 | 29 ÷ 26 = 1 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 113 | 7571 |
| 32 and 87 | 2784 |
| 157 and 178 | 27946 |
| 51 and 85 | 255 |
| 29 and 97 | 2813 |