Least Common Multiple (LCM) of 13 and 142
The least common multiple (LCM) of 13 and 142 is 1846.
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 13 and 142?
First, calculate the GCD of 13 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 142 = 0 remainder 13 |
| 2 | 142 ÷ 13 = 10 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 123 | 19803 |
| 198 and 48 | 1584 |
| 128 and 180 | 5760 |
| 172 and 36 | 1548 |
| 152 and 74 | 5624 |