Least Common Multiple (LCM) of 142 and 176
The least common multiple (LCM) of 142 and 176 is 12496.
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 176?
First, calculate the GCD of 142 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 176 = 0 remainder 142 |
| 2 | 176 ÷ 142 = 1 remainder 34 |
| 3 | 142 ÷ 34 = 4 remainder 6 |
| 4 | 34 ÷ 6 = 5 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 116 | 14964 |
| 175 and 36 | 6300 |
| 192 and 158 | 15168 |
| 73 and 160 | 11680 |
| 162 and 72 | 648 |