Least Common Multiple (LCM) of 142 and 75
The least common multiple (LCM) of 142 and 75 is 10650.
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 75?
First, calculate the GCD of 142 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 75 = 1 remainder 67 |
| 2 | 75 ÷ 67 = 1 remainder 8 |
| 3 | 67 ÷ 8 = 8 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 197 | 38415 |
| 54 and 14 | 378 |
| 80 and 106 | 4240 |
| 138 and 124 | 8556 |
| 149 and 19 | 2831 |