Least Common Multiple (LCM) of 104 and 142
The least common multiple (LCM) of 104 and 142 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 104 and 142?
First, calculate the GCD of 104 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 142 = 0 remainder 104 |
| 2 | 142 ÷ 104 = 1 remainder 38 |
| 3 | 104 ÷ 38 = 2 remainder 28 |
| 4 | 38 ÷ 28 = 1 remainder 10 |
| 5 | 28 ÷ 10 = 2 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 200 | 2600 |
| 111 and 128 | 14208 |
| 42 and 21 | 42 |
| 22 and 93 | 2046 |
| 186 and 105 | 6510 |