Least Common Multiple (LCM) of 142 and 104
The least common multiple (LCM) of 142 and 104 is 7384.
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 104?
First, calculate the GCD of 142 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 104 = 1 remainder 38 |
| 2 | 104 ÷ 38 = 2 remainder 28 |
| 3 | 38 ÷ 28 = 1 remainder 10 |
| 4 | 28 ÷ 10 = 2 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 71 | 2272 |
| 33 and 32 | 1056 |
| 175 and 55 | 1925 |
| 74 and 28 | 1036 |
| 34 and 58 | 986 |