Least Common Multiple (LCM) of 142 and 42
The least common multiple (LCM) of 142 and 42 is 2982.
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 42?
First, calculate the GCD of 142 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 42 = 3 remainder 16 |
| 2 | 42 ÷ 16 = 2 remainder 10 |
| 3 | 16 ÷ 10 = 1 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 99 | 1980 |
| 79 and 115 | 9085 |
| 145 and 180 | 5220 |
| 70 and 188 | 6580 |
| 176 and 96 | 1056 |